Will and Ivan went shopping with a total amount of $140. They had $112 left after shopping. Will's remaining money was 3 times the amount he paid for. Ivan's remaining money was 5 times the amount he had spent.
- How much did Ivan spend?
- How much did Ivan bring along for shopping?
| |
Will |
Ivan |
Total |
| Before |
4 u |
6 p |
140 |
| Change |
- 1 u |
- 1 p |
- 28 |
| After |
3 u |
5 p |
112 |
(a)
Amount that Will and Ivan spent
= 140 - 112
= $28
Amount that Will and Ivan spent
= 1 u + 1 p
1 u + 1 p = 28
1 u = 28 - 1 p --- (1)
Amount that Will and Ivan had left
= 3 u + 5 p
3 u + 5 p = 112
3 u = 112 - 5 p --- (2)
Make u the same.
(1)
x 3 3 u = 84 - 3 p --- (3)
(3) = (2)
84 - 3 p = 112 - 5 p
5 p - 3 p = 112 - 84
2 p = 28
1 p = 28 ÷ 2 = 14
Amount that Ivan spent = $14
(b)
Amount that Ivan brought along
= 6 p
= 6 x 14
= $84
Answer(s): (a) $14; (b) $84
