Rael and Owen went shopping with a total amount of $370. They had $296 left after shopping. Rael's remaining money was 3 times the amount he paid for. Owen's remaining money was 5 times the amount he had spent.
- How much did Owen spend?
- How much did Owen bring along for shopping?
| |
Rael |
Owen |
Total |
| Before |
4 u |
6 p |
370 |
| Change |
- 1 u |
- 1 p |
- 74 |
| After |
3 u |
5 p |
296 |
(a)
Amount that Rael and Owen spent
= 370 - 296
= $74
Amount that Rael and Owen spent
= 1 u + 1 p
1 u + 1 p = 74
1 u = 74 - 1 p --- (1)
Amount that Rael and Owen had left
= 3 u + 5 p
3 u + 5 p = 296
3 u = 296 - 5 p --- (2)
Make u the same.
(1)
x 3 3 u = 222 - 3 p --- (3)
(3) = (2)
222 - 3 p = 296 - 5 p
5 p - 3 p = 296 - 222
2 p = 74
1 p = 74 ÷ 2 = 37
Amount that Owen spent = $37
(b)
Amount that Owen brought along
= 6 p
= 6 x 37
= $222
Answer(s): (a) $37; (b) $222
