Luke and Bobby went shopping with a total amount of $310. They had $248 left after shopping. Luke's remaining money was 3 times the amount he paid for. Bobby's remaining money was 5 times the amount he had spent.
- How much did Bobby spend?
- How much did Bobby bring along for shopping?
| |
Luke |
Bobby |
Total |
| Before |
4 u |
6 p |
310 |
| Change |
- 1 u |
- 1 p |
- 62 |
| After |
3 u |
5 p |
248 |
(a)
Amount that Luke and Bobby spent
= 310 - 248
= $62
Amount that Luke and Bobby spent
= 1 u + 1 p
1 u + 1 p = 62
1 u = 62 - 1 p --- (1)
Amount that Luke and Bobby had left
= 3 u + 5 p
3 u + 5 p = 248
3 u = 248 - 5 p --- (2)
Make u the same.
(1)
x 3 3 u = 186 - 3 p --- (3)
(3) = (2)
186 - 3 p = 248 - 5 p
5 p - 3 p = 248 - 186
2 p = 62
1 p = 62 ÷ 2 = 31
Amount that Bobby spent = $31
(b)
Amount that Bobby brought along
= 6 p
= 6 x 31
= $186
Answer(s): (a) $31; (b) $186
