WISKUNDIGE GELETTERDHEID
Graad 10
NOG OEFENINGE
Koers, verhouding en eweredigheid : antwoorde
  
MATHEMATICAL LITERACY
Grade 10
MORE EXERCISES
Rate, ratio and proportion : answers
  
  
  
Antwoorde / Answers  1
  
     
$$ \hspace*{6 mm}\mathrm{1.1\kern2mmMeer\ aartappels\ sal\ meer\ kos.\ \kern30mm } $$
[ V 1. ]
     
$$ \hspace*{6 mm}\mathrm{1.2\kern2mmDirekte\ eweredigheid. \kern30mm } $$
[ V 1. ]
     
$$ \hspace*{6 mm}\mathrm{1.3\kern2mm4\ kg\ aartappels\ kos\ R\ 28,45. \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{1\ kg\ aartappels\ kos\ R\ \frac{28,45}{4}. \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{15\ kg\ aartappels\ kos\ R\ \frac{28,45}{4}\ \times\ 15 \kern30mm } $$

$$ \hspace*{43 mm}\mathrm{d.i.\ R\ 106,69 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{15\ kg\ aartappels\ kos\ R\ 106,69 \kern30mm } $$
[ V 1. ]
     
$$ \hspace*{6 mm}\mathrm{1.4\kern2mmR\ 28,45\ koop\ 4\ kg\ aartappels. \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{R\ 1\ koop\ \frac{4}{28,45}\ kg\ aartappels. \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{R\ 77,10\ koop\ \frac{4}{28,45}\ \times\ 77,10\ kg \kern30mm } $$

$$ \hspace*{36 mm}\mathrm{i.e.\ 10,84\ kg \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{10,84\ kg\ aartappels\ kos\ R\ 77,10 \kern30mm } $$
[ V 1. ]
     
$$ \hspace*{6 mm}\mathrm{1.1\kern2mmMore\ potatoes\ will\ cost\ more.\ \kern30mm } $$
[ Q 1. ]
     
$$ \hspace*{6 mm}\mathrm{1.2\kern2mmDirect\ proportion. \kern30mm } $$
[ Q 1. ]
     
$$ \hspace*{6 mm}\mathrm{1.3\kern2mm4\ kg\ potatoes\ cos\ R\ 28,45. \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{1\ kg\ potatoes\ costs\ R\ \frac{28,45}{4}. \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{15\ kg\ potatoes\ cost\ R\ \frac{28,45}{4}\ \times\ 15 \kern30mm } $$

$$ \hspace*{43 mm}\mathrm{i.e.\ R\ 106,69 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{15\ kg\ potatoes\ cost\ R\ 106,69 \kern30mm } $$
[ Q 1. ]
     
$$ \hspace*{6 mm}\mathrm{1.4\kern2mmR\ 28,45\ buys\ 4\ kg\ potatoes. \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{R\ 1\ buys\ \frac{4}{28,45}\ kg\ potatoes. \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{R\ 77,10\ buys\ \frac{4}{28,45}\ \times\ 77,10\ kg \kern30mm } $$

$$ \hspace*{36 mm}\mathrm{i.e.\ 10,84\ kg \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{10,84\ kg\ potatoes\ cost\ R\ 77,10 \kern30mm } $$
[ Q 1. ]
  
  
Antwoorde / Answers  2
  
     
$$ \hspace*{6 mm}\mathrm{2.1\kern2mm3\ pampoene\ kos\ R\ 38,25 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{1\ pampoen\ kos\ R\ \frac{38,25}{3} \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{8\ pampoene\ kos\ R\ \frac{38,25}{3}\ \times\ 8 \kern30mm } $$
$$ \hspace*{36 mm}\mathrm{i.e.\ R\ 102,00 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{8\ pampoene\ kos\ R\ 102,00 \kern30mm } $$
[ V 1. ]
     
$$ \hspace*{6 mm}\mathrm{2.2\kern2mmR\ 38,25\ koop\ 3\ pampoene \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{R\ 1\ koop\ \frac{3}{38,25}\ pampoene \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{R\ 63,75\ koop\ \frac{3}{38,25}\ \times\ 8\ pampoene \kern30mm } $$

$$ \hspace*{36 mm}\mathrm{i.e.\ 5 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{R\ 63,75\ koop\ 5\ pampoene \kern30mm } $$
[ V 2. ]
     
$$ \hspace*{6 mm}\mathrm{2.1\kern2mm3\ pampoene\ kos\ R\ 38,25 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{1\ pumpkin\ costs\ R\ \frac{38,25}{3} \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{8\ pumpkins\ cost\ R\ \frac{38,25}{3}\ \times\ 8 \kern30mm } $$
$$ \hspace*{38 mm}\mathrm{i.e.\ R\ 102,00 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{8\ pumpkins\ cost\ R\ 102,00 \kern30mm } $$
[ Q 2. ]
     
$$ \hspace*{6 mm}\mathrm{2.2\kern2mmR\ 38,25\ buys\ 3\ pumpkins \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{R\ 1\ buys\ \frac{3}{38,25}\ pumpkins \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{R\ 63,75\ buys\ \frac{3}{38,25}\ \times\ 63,75\ pumpkins \kern30mm } $$

$$ \hspace*{37 mm}\mathrm{i.e.\ 5 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{R\ 63,75\ buys\ 5\ pumpkins \kern30mm } $$
[ Q 2. ]
  
  
Antwoorde / Answers  3
  
     
$$ \hspace*{6 mm}\mathrm{3.1\kern2mm34,25\ \ell\ petrol\ kos\ R\ 655,55 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{1\ \ell\ petrol\ kos\ R\ \frac{655,55}{34,25} \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{68,21\ \ell\ petrol\ kos\ R\frac{655,55}{34,25}\times 68,21 \kern30mm } $$
$$ \hspace*{37 mm}\mathrm{d.i.\ R\ 1\ 305,55 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{68,21\ \ell\ petrol\ kos\ R\ 1\ 305,55 \kern30mm } $$
[ V 3. ]
     
$$ \hspace*{6 mm}\mathrm{3.2\kern2mmR\ 655,55\ koop 34,25\ \ell\ petrol \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{R\ 1\ koop\ \frac{34,25}{655,55} \ell\ petrol \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{R\ 816,20\ koop\ \frac{34,25}{655,55}\times 816,20\ \ell\ petrol } $$
$$ \hspace*{37 mm}\mathrm{d.i.\ 42,643 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{R\ 816,20\ koop\ 42,643\ \ell\ petrol \kern30mm } $$
[ V 3. ]
     
$$ \hspace*{6 mm}\mathrm{3.1\kern2mm34,25\ \ell\ petrol\ costs\ R\ 655,55 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{1\ \ell\ petrol\ costs\ R\ \frac{655,55}{34,25} \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{68,21\ \ell\ petrol\ costs\ R\ \frac{655,55}{34,25}\ \times\ 8 \kern30mm } $$
$$ \hspace*{38 mm}\mathrm{i.e.\ R\ 1\ 305,55 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{68,21\ \ell\ petrol\ costs\ R\ 1\ 305,55 \kern30mm } $$
[ Q 3. ]
     
$$ \hspace*{6 mm}\mathrm{3.2\kern2mmR\ 655,55\ buys 34,25\ \ell\ petrol \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{R\ 1\ buys\ \frac{34,25}{655,55} \ell\ petrol \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{R\ 816,20\ buys\ \frac{34,25}{655,55}\times 816,20\ \ell\ petrol } $$
$$ \hspace*{37 mm}\mathrm{d.i.\ 42,643 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{R\ 816,20\ buys\ 42,643\ \ell\ petrol \kern30mm } $$
[ Q 3. ]
  
  
Antwoorde / Answers  4
  
     
$$ \hspace*{6 mm}\mathrm{4.1\kern2mm9\ km\ in\ 36,5\ minute \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{1\ km\ in\ \frac{36,5}{9}\ minute \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{21\ km\ in\ \frac{36,5}{9}\ \times\ 21 \kern30mm } $$
$$ \hspace*{24 mm}\mathrm{i.e.\ 85,17\ minute \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{21\ km\ in\ 85,17\ minute \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{21\ km\ in\ 1\ h\ 25,17\ m \kern30mm } $$
[ V 4. ]
     
$$ \hspace*{6 mm}\mathrm{4.2\kern2mmIn\ 36,5\ minute\ hardloop\ hy\ 9\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{In\ 1\ minuut\ hadloop\ hy\ \frac{9}{36,5}\ km \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{In\ 55,8\ min\ hadloop\ hy\ \frac{9}{36,5}\times 55,8\ km \kern30mm } $$

$$ \hspace*{44 mm}\mathrm{d.i.\ 13,759 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{In\ 55,8\ minute\ hadloop\ hy\ 13,759\ km \kern30mm } $$

[ V 4. ]
     
$$ \hspace*{6 mm}\mathrm{4.1\kern2mm9\ km\ in\ 36,5\ minutes \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{1\ km\ in\ \frac{36,5}{9}\ minutes \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{21\ km\ in\ \frac{36,5}{9}\ \times\ 21 \kern30mm } $$
$$ \hspace*{24 mm}\mathrm{i.e.\ 85,17\ minutes \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{21\ km\ in\ 85,17\ minutes \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{21\ km\ in\ 1\ h\ 25,17\ m \kern30mm } $$
[ Q 4. ]
     
$$ \hspace*{6 mm}\mathrm{4.2\kern2mmIn\ 36,5\ minutes\ he\ runs\ 9\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{In\ 1\ minute\ he\ runs\ \frac{9}{36,5}\ km \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{In\ 55,8\ minutes\ he\ runs\ \frac{9}{36,5}\times 55,8\ km \kern30mm } $$

$$ \hspace*{44 mm}\mathrm{d.i.\ 13,759 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{In\ 55,8\ minute\ he\ runs\ 13,759\ km \kern30mm } $$

[ Q 4. ]
  
  
Antwoorde / Answers  5
  
     
$$ \hspace*{6 mm}\mathrm{5.1\kern2mmIn\ 33,4375\ minute\ ry\ dit\ 53,5\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{In\ 1\ minuut\ ry\ dit\ \frac{53,5}{33,4375}\ km \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{In\ 60\ minute\ ry\ dit\ \frac{53,5}{33,4375}\ \times\ 60 \kern30mm } $$
$$ \hspace*{38 mm}\mathrm{d.i.\ 96\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Spoed\ van\ motor\ is\ 96\ km/h \kern30mm } $$
[ V 5. ]
     
$$ \hspace*{6 mm}\mathrm{5.2\kern2mmIn\ 33,4375\ minute\ ry\ dit\ 53,5\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{In\ 1\ minuut\ ry\ dit\ \frac{53,5}{33,4375}\ km \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{In\ 3,5\times 60\ minute\ ry\ dit\ \frac{53,5}{33,4375}\ \times\ 3,5\times 60 \kern30mm } $$
$$ \hspace*{48 mm}\mathrm{d.i.\ 336\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Afstand\ gery\ is\ 336\ km \kern30mm } $$
[ V 5. ]
$$ \hspace*{38 mm}\mathrm{\bold O\bold F \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{In\ 1\ uur\ ry\ dit\ 96\ km\ \dotsb\ 5.1 \kern30mm } $$ $$ \hspace*{13 mm}\mathrm{In\ 3,5\ uur\ ry\ dit\ 96\ \times\ 3,5 km\ \kern30mm } $$
$$ \hspace*{36 mm}\mathrm{d.i.\ 336\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Afstand\ gery\ is\ 336\ km \kern30mm } $$
[ V 5. ]
     
$$ \hspace*{6 mm}\mathrm{5.3\kern2mmDit\ ry\ 53,5\ km\ in\ 33,4375\ minute \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Dit\ ry\ 1\ km\ in\ \frac{33,4375}{53,5}\ minute \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{Dit\ ry\ 38,7\ km\ in\ \frac{33,4375}{53,5}\ \times 38,7\ minute \kern30mm } $$

$$ \hspace*{42 mm}\mathrm{d.i.\ 24,19\ minute \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Dit\ neem\ 24,19\ minute\ om\ 38,7\ km\ te\ ry. \kern30mm } $$
[ V 5. ]
$$ \hspace*{38 mm}\mathrm{\bold O\bold F \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Dit\ ry\ 96\ km\ in\ 60\ minute \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Dit\ ry\ 1\ km\ in\ \frac{60}{96}\ minute \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Dit\ ry\ 38,7\ km\ in\ \frac{60}{96}\ \times\ 38,7\ minute \kern30mm } $$

$$ \hspace*{34 mm}\mathrm{d.i.\ 24,19\ minute \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Dit\ ry\ 38,7\ km\ in\ \frac{60}{96}\ \times\ 38,7\ minute \kern30mm } $$
[ V 5. ]
     
$$ \hspace*{6 mm}\mathrm{5.1\kern2mmIn\ 33,4375\ minutes\ it\ travels\ 53,5\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{In\ 1\ minute\ it\ travels\ \frac{53,5}{33,4375}\ km \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{In\ 60\ minutes\ it\ travels\ \frac{53,5}{33,4375}\ \times\ 60 \kern30mm } $$
$$ \hspace*{46 mm}\mathrm{d.i.\ 96\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Speed\ of\ car\ is\ 96\ km/h \kern30mm } $$
[ Q 5. ]
     
$$ \hspace*{6 mm}\mathrm{5.2\kern2mmIn\ 33,4375\ minutes\ it\ travels\ 53,5\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{In\ 1\ minute\ it\ travels\ \frac{53,5}{33,4375}\ km \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{In\ 3,5\times 60\ minutes\ it\ travels\ \frac{53,5}{33,4375}\ \times\ 3,5\times 60 \kern30mm } $$
$$ \hspace*{56 mm}\mathrm{d.i.\ 336\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Distance\ travelled\ is\ 336\ km \kern30mm } $$
[ Q 5. ]
$$ \hspace*{38 mm}\mathrm{\bold O\bold R \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{In\ 1\ hour\ it\ travels\ 96\ km\ \dotsb\ 5.1 \kern30mm } $$ $$ \hspace*{13 mm}\mathrm{In\ 3,5\ hours\ it\ travels\ 96\ \times\ 3,5 km\ \kern30mm } $$
$$ \hspace*{46 mm}\mathrm{d.i.\ 336\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Distance\ travelled\ \ is\ 336\ km \kern30mm } $$
[ Q 5. ]
     
$$ \hspace*{6 mm}\mathrm{5.3\kern2mmIt\ travels\ 53,5\ km\ in\ 33,4375\ minutes \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{It\ travels\ 1\ km\ in\ \frac{33,4375}{53,5}\ minutes \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{It\ travels\ 38,7\ km\ in\ \frac{33,4375}{53,5}\ \times 38,7\ minutes \kern30mm } $$

$$ \hspace*{42 mm}\mathrm{d.i.\ 24,19\ minutes \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{It\ takes\ 24,19\ minutes\ to\ travel\ 38,7\ km \kern30mm } $$
[ Q 5. ]
$$ \hspace*{38 mm}\mathrm{\bold O\bold R \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{It\ travels\ 96\ km\ in\ 60\ minutes \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{It\ travels\ 1\ km\ in\ \frac{60}{96}\ minutes \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{It\ travels\ 38,7\ km\ in\ \frac{60}{96}\ \times 38,7\ minutes \kern30mm } $$

$$ \hspace*{40 mm}\mathrm{d.i.\ 24,19\ minutes \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{It\ takes\ 24,19\ minutes\ to\ travel\ 38,7\ km \kern30mm } $$
[ Q 5. ]
  
  
Antwoorde / Answers  6
  
     
$$ \hspace*{6 mm}\mathrm{6.1\kern2mm1\ brood\ lewer\ 17\ snye. \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{6\ brode\ lewer\ 6\ \times 17\ snye. \kern30mm } $$
$$ \hspace*{38 mm}\mathrm{d.i.\ 102\ snye \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{3\ snye\ voed\ 1\ kind, \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{1\ sny\ voed\ \frac{1}{3}\ kind, \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{102\ snye\ voed\ \frac{1}{3}\ \times 102\ kinders \kern30mm } $$
$$ \hspace*{38 mm}\mathrm{d.i.\ 34\ kinders \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{6\ brode\ voed\ 34\ kinders \kern30mm } $$
[ V 6. ]
     
$$ \hspace*{6 mm}\mathrm{6.1\kern2mm1\ loaf\ of\ bread\ gives\ 17\ slices. \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{6\ loaves\ gives\ 6\ \times 17\ slices. \kern30mm } $$
$$ \hspace*{38 mm}\mathrm{i.e.\ 102\ slices \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{3\ slices\ feed\ 1\ child, \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{1\ slice\ feeds\ \frac{1}{3}\ child, \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{102\ slices\ feed\ \frac{1}{3}\ \times 102\ children \kern30mm } $$
$$ \hspace*{38 mm}\mathrm{d.i.\ 34\ children \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{6\ loaves\ of\ bread\ feed\ 34\ children. \kern30mm } $$
[ Q 6. ]
  
  
Antwoorde / Answers  7
  
     
$$ \hspace*{6 mm}\mathrm{7.1\kern2mmmeer\ liter\ is\ nodig. \kern30mm } $$
[ V 7. ]
     
$$ \hspace*{6 mm}\mathrm{7.2\kern2mmDirekte\ eweredigheid. \kern30mm } $$
[ V 7. ]
     
$$ \hspace*{6 mm}\mathrm{7.3\kern2mm31,947\ km\ gebruik\ 2,3\ \ell \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{1\ km\ gebruik\ \frac{2,3}{31,947}\ \ell \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{100\ km\ gebruik\ \frac{2,3}{31,947}\ \times\ 100 \ell \kern30mm } $$
$$ \hspace*{34 mm}\mathrm{d.i.\ 7,199 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{100\ km\ gebruik\ 7,199\ \ell \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{7,199\ \ell\ is nodig\ om\ 100\ km\ te\ reis. \kern30mm } $$
[ V 7. ]
     
$$ \hspace*{6 mm}\mathrm{7.4\kern2mm2,3\ \ell\ is\ nodig\ vir\ 31,947\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{1\ \ell\ is\ nodig\ vir\ \frac{31,947}{2,3}\ km \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{18,6\ \ell\ is\ nodig\ vir\ \frac{31,947}{2,3}\ \times\ 18,6 km \kern30mm } $$

$$ \hspace*{36 mm}\mathrm{d.i.\ 258,354\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{18,6\ \ell\ is\ nodig\ vir\ 258,354\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Afstand\ gery\ met\ 18,6\ \ell\ is\ 258,354\ km \kern30mm } $$
[ V 7. ]
     
$$ \hspace*{6 mm}\mathrm{7.1\kern2mmMore\ liters\ are\ required. \kern30mm } $$
[ Q 7. ]
     
$$ \hspace*{6 mm}\mathrm{7.2\kern2mmDirect\ proportion. \kern30mm } $$
[ Q 7. ]
     
$$ \hspace*{6 mm}\mathrm{7.3\kern2mm31,947\ km\ use\ 2,3\ \ell \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{1\ km\ uses\ \frac{2,3}{31,947}\ \ell \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{100\ km\ use\ \frac{2,3}{31,947}\ \times\ 100 \ell \kern30mm } $$
$$ \hspace*{32 mm}\mathrm{i.e.\ 7,199 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{100\ km\ use\ 7,199\ \ell \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{7,199\ \ell\ is needed\ to\ travel\ 100\ km \kern30mm } $$
[ Q 7. ]
     
$$ \hspace*{6 mm}\mathrm{7.4\kern2mm2,3\ \ell\ is\ needed\ for\ 31,947\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{1\ \ell\ is\ needed\ for\ \frac{31,947}{2,3}\ km \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{18,6\ \ell\ is\ needed\ for\ \frac{31,947}{2,3}\ \times\ 18,6 km \kern30mm } $$

$$ \hspace*{38 mm}\mathrm{d.i.\ 258,354\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{18,6\ \ell\ is\ needed\ for\ 258,354\ km \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Distance\ travelled\ with\ 18,6\ \ell\ is\ 258,354\ km \kern30mm } $$
[ Q 7. ]

  
  
Antwoorde / Answers  8
  
     
$$ \hspace*{6 mm}\mathrm{8.1\kern2mm1\ koppie\ =\ 147\ g \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{2\ koppies\ =\ 147\ \times\ 2\ g \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{d.i.\ 294\ g\ <\ 300\ g \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Sy\ het\ genoeg\ meel. \kern30mm } $$
[ V 8. ]
     
$$ \hspace*{6 mm}\mathrm{8.1\kern2mm1\ koppie\ melk\ =\ 250\ m\ell \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{\frac12\ koppie\ =\ 250\ \times\ \frac12\ m\ell \kern30mm } $$
$$ \hspace*{29 mm}\mathrm{=\ 125\ m\ell \kern30mm } $$
[ V 8. ]
     
$$ \hspace*{6 mm}\mathrm{8.3\kern2mm1\ teelepel\ =\ 5\ m\ell \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{3\ teelepels\ =\ 3\ \times\ 5\ m\ell \kern30mm } $$
$$ \hspace*{32 mm}\mathrm{=\ 15\ m\ell \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{250\ m\ell\ suiker\ weeg\ 200\ g \kern30mm } $$
$$ \hspace*{17 mm}\mathrm{1\ m\ell\ of\ suiker\ weeg\ \frac{200}{250}\ g \kern30mm } $$

$$ \hspace*{15 mm}\mathrm{15\ m\ell\ of\ suiker\ weeg\ \frac{200}{250}\ \times\ 15 g \kern30mm } $$
$$ \hspace*{45 mm}\mathrm{d.i.\ 12\ g \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Sy\ moet\ 12\ g\ suiker\ gebruik.. \kern30mm } $$
[ V 8. ]
     
$$ \hspace*{6 mm}\mathrm{8.4\kern2mmT\ =\ \frac{5}{9}(450\ ─\ 32)\ ℃ \kern30mm } $$
$$ \hspace*{17 mm}\mathrm{=\ 232,22\ ℃ \kern30mm } $$
[ V 8. ]
     
$$ \hspace*{6 mm}\mathrm{8.1\kern2mm1\ cup\ =\ 147\ g \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{2\ cups\ =\ 147\ \times\ 2\ g \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{i.e.\ 294\ g\ <\ 300\ g \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{She\ has\ enough\ flour. \kern30mm } $$
[ Q 8. ]
     
$$ \hspace*{6 mm}\mathrm{8.2\kern2mm1\ cup\ of\ milk\ =\ 250\ m\ell \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{\frac12\ cup\ =\ 250\ \times\ \frac12\ m\ell \kern30mm } $$
$$ \hspace*{25 mm}\mathrm{=\ 125\ m\ell \kern30mm } $$
[ Q 8. ]
     
$$ \hspace*{6 mm}\mathrm{8.3\kern2mm1\ teaspoon\ =\ 5\ m\ell \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{3\ teaspoons\ =\ 3\ \times\ 5\ m\ell \kern30mm } $$
$$ \hspace*{35 mm}\mathrm{=\ 15\ m\ell \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{250\ m\ell\ of\ sugar\ weighs\ 200\ g \kern30mm } $$
$$ \hspace*{17 mm}\mathrm{1\ m\ell\ of\ sugar\ weighs\ \frac{200}{250}\ g \kern30mm } $$

$$ \hspace*{15 mm}\mathrm{15\ m\ell\ of\ sugar\ weighs\ \frac{200}{250}\ \times\ 15 g \kern30mm } $$
$$ \hspace*{49 mm}\mathrm{i.e.\ 12\ g \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{She\ should\ use\ 12\ g\ of\ sugar. \kern30mm } $$
[ Q 8. ]
     
$$ \hspace*{6 mm}\mathrm{8.4\kern2mmT\ =\ \frac{5}{9}(450\ ─\ 32)\ ℃ \kern30mm } $$
$$ \hspace*{17 mm}\mathrm{=\ 232,22\ ℃ \kern30mm } $$
[ Q 8. ]
  
  
Antwoorde / Answers  99998
  
     
$$ \hspace*{6 mm}\mathrm{9.1\kern2mm2\ m\ell\ konsentraat\ by\ 5\ m\ell\ water \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{1\ m\ell\ konsentraat\ by\ \frac{5}{2}\ m\ell\ water \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{50\ m\ell\ konsentraat\ by\ \frac{5}{2}\times 50\ m\ell\ water \kern30mm } $$
$$ \hspace*{45 mm}\mathrm{d.i.\ 125 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{By\ 50\ m\ell\ konsentraat\ word\ 125\ m\ell \kern30mm } $$ $$ \hspace*{13 mm}\mathrm{water\ gevoeg. \kern30mm } $$

[ V 9. ]
     
$$ \hspace*{6 mm}\mathrm{9.2\kern2mmMeng\ 5\ m\ell\ water\ met\ 2\ m\ell\ konsentraat \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Meng\ 1\ m\ell\ water\ with\ \frac{2}{5}\ m\ell\ konsentraat \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{Meng\ 500\ m\ell\ water\ with\ \frac{2}{5}\times 500\ m\ell\ konsentraat \kern30mm } $$

$$ \hspace*{50 mm}\mathrm{i.e.\ 200 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{500\ m\ell\ water\ word\ gemeng\ met\ \kern30mm } $$ $$ \hspace*{13 mm}\mathrm{200\ m\ell\ konsentraat. \kern30mm } $$

[ V 9. ]
     
$$ \hspace*{6 mm}\mathrm{9.3\kern2mm7\ \ell\ koeldrank\ word\ gemaak\ deur\ 2\ \ell \kern30mm } $$ $$ \hspace*{13 mm}\mathrm{konsentraat\ met\ 5\ \ell\ water\ te\ meng. \kern30mm } $$

$$ \hspace*{15 mm}\mathrm{Totale\ \kern8mm\ volume \kern5mm\ volume \kern30mm } $$ $$ \hspace*{13 mm}\mathrm{volume\ \kern3mm\ konsentraat\ \kern3mm\ water \kern30mm } $$ $$ \hspace*{18 mm}\mathrm{7\ \kern15mm\ 2\ \kern15mm\ 5 \kern30mm } $$


$$ \hspace*{18 mm}\mathrm{1\ \kern14mm\ \frac{2}{7}\ \kern15mm\ \frac{5}{7} \kern30mm } $$

$$ \hspace*{18 mm}\mathrm{3\ \kern10mm\ \frac{2}{7}\times\ 3 \kern10mm\ \frac{5}{7}\times\ 3 \kern30mm } $$

$$ \hspace*{18 mm}\mathrm{3\ \kern14mm\ \frac{6}{7}\ \kern15mm\ \frac{15}{7} \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{Meng\ 857\ m\ell\ konsentraat\ met \kern30mm } $$ $$ \hspace*{13 mm}\mathrm{2,143\ \ell\ water. \kern30mm } $$

[ V 9. ]
     
$$ \hspace*{6 mm}\mathrm{9.1\kern2mmMix\ 2\ m\ell\ concentrate\ with\ 5\ m\ell\ water \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Mix\ 1\ m\ell\ concentrate\ with\ \frac{5}{2}\ m\ell\ water \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{50\ m\ell\ concentrate\ with\ \frac{5}{2}\times 50\ m\ell\ water \kern30mm } $$
$$ \hspace*{48 mm}\mathrm{i.e.\ 125 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Add\ 125\ m\ell\ of\ water\ to\ 50\ m\ell \kern30mm } $$ $$ \hspace*{13 mm}\mathrm{of\ concentrate. \kern30mm } $$

[ Q 9. ]
     
$$ \hspace*{6 mm}\mathrm{9.2\kern2mmMix\ 5\ m\ell\ water\ with\ 2\ m\ell\ concentrate \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{Mix\ 1\ m\ell\ water\ with\ \frac{2}{5}\ m\ell\ concentrate \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{Mix\ 500\ m\ell\ water\ with\ \frac{2}{5}\times 500\ m\ell\ concentrate \kern30mm } $$

$$ \hspace*{48 mm}\mathrm{i.e.\ 200 \kern30mm } $$
$$ \hspace*{13 mm}\mathrm{500\ m\ell\ of\ water\ is\ mixed\ with \kern30mm } $$ $$ \hspace*{13 mm}\mathrm{200\ m\ell\ concentrate. \kern30mm } $$

[ Q 9. ]
     
$$ \hspace*{6 mm}\mathrm{9.3\kern2mm7\ \ell\ of\ cold\ drink\ is\ made\ from\ 2\ \ell\ of \kern30mm } $$ $$ \hspace*{13 mm}\mathrm{concentrate\ and\ 5\ \ell\ of\ water. \kern30mm } $$

$$ \hspace*{15 mm}\mathrm{Total\ \kern8mm\ volume \kern5mm\ volume \kern30mm } $$ $$ \hspace*{13 mm}\mathrm{volume\ \kern2mm\ concentrate\ \kern2mm\ water \kern30mm } $$ $$ \hspace*{18 mm}\mathrm{7\ \kern15mm\ 2\ \kern15mm\ 5 \kern30mm } $$


$$ \hspace*{18 mm}\mathrm{1\ \kern14mm\ \frac{2}{7}\ \kern15mm\ \frac{5}{7} \kern30mm } $$

$$ \hspace*{18 mm}\mathrm{3\ \kern10mm\ \frac{2}{7}\times\ 3 \kern10mm\ \frac{5}{7}\times\ 3 \kern30mm } $$

$$ \hspace*{18 mm}\mathrm{3\ \kern14mm\ \frac{6}{7}\ \kern15mm\ \frac{15}{7} \kern30mm } $$

$$ \hspace*{13 mm}\mathrm{Mix\ 857\ m\ell\ of\ concentrate\ with \kern30mm } $$ $$ \hspace*{13 mm}\mathrm{2,143\ \ell\ of\ water. \kern30mm } $$

[ Q 9. ]