Peter and Ben went shopping with a total amount of $403. They had $341 left after shopping. Peter's remaining money was 4 times the amount he paid for. Ben's remaining money was 7 times the amount he had spent.
- How much did Ben spend?
- How much did Ben bring along for shopping?
|
Peter |
Ben |
Total |
Before |
5 u |
8 p |
403 |
Change |
- 1 u |
- 1 p |
- 62 |
After |
4 u |
7 p |
341 |
(a)
Amount that Peter and Ben spent
= 403 - 341
= $62
Amount that Peter and Ben spent
= 1 u + 1 p
1 u + 1 p = 62
1 u = 62 - 1 p --- (1)
Amount that Peter and Ben had left
= 4 u + 7 p
4 u + 7 p = 341
4 u = 341 - 7 p --- (2)
Make u the same.
(1)
x 4 4 u = 248 - 4 p --- (3)
(3) = (2)
248 - 4 p = 341 - 7 p
7 p - 4 p = 341 - 248
3 p = 93
1 p = 93 ÷ 3 = 31
Amount that Ben spent = $31
(b)
Amount that Ben brought along
= 8 p
= 8 x 31
= $248
Answer(s): (a) $31; (b) $248