Ben and Liam went shopping with a total amount of $290. They had $232 left after shopping. Ben's remaining money was 3 times the amount he paid for. Liam's remaining money was 5 times the amount he had spent.
- How much did Liam spend?
- How much did Liam bring along for shopping?
|
Ben |
Liam |
Total |
Before |
4 u |
6 p |
290 |
Change |
- 1 u |
- 1 p |
- 58 |
After |
3 u |
5 p |
232 |
(a)
Amount that Ben and Liam spent
= 290 - 232
= $58
Amount that Ben and Liam spent
= 1 u + 1 p
1 u + 1 p = 58
1 u = 58 - 1 p --- (1)
Amount that Ben and Liam had left
= 3 u + 5 p
3 u + 5 p = 232
3 u = 232 - 5 p --- (2)
Make u the same.
(1)
x 3 3 u = 174 - 3 p --- (3)
(3) = (2)
174 - 3 p = 232 - 5 p
5 p - 3 p = 232 - 174
2 p = 58
1 p = 58 ÷ 2 = 29
Amount that Liam spent = $29
(b)
Amount that Liam brought along
= 6 p
= 6 x 29
= $174
Answer(s): (a) $29; (b) $174