Justin and Tim went shopping with a total amount of $320. They had $256 left after shopping. Justin's remaining money was 3 times the amount he paid for. Tim's remaining money was 5 times the amount he had spent.
- How much did Tim spend?
- How much did Tim bring along for shopping?
| |
Justin |
Tim |
Total |
| Before |
4 u |
6 p |
320 |
| Change |
- 1 u |
- 1 p |
- 64 |
| After |
3 u |
5 p |
256 |
(a)
Amount that Justin and Tim spent
= 320 - 256
= $64
Amount that Justin and Tim spent
= 1 u + 1 p
1 u + 1 p = 64
1 u = 64 - 1 p --- (1)
Amount that Justin and Tim had left
= 3 u + 5 p
3 u + 5 p = 256
3 u = 256 - 5 p --- (2)
Make u the same.
(1)
x 3 3 u = 192 - 3 p --- (3)
(3) = (2)
192 - 3 p = 256 - 5 p
5 p - 3 p = 256 - 192
2 p = 64
1 p = 64 ÷ 2 = 32
Amount that Tim spent = $32
(b)
Amount that Tim brought along
= 6 p
= 6 x 32
= $192
Answer(s): (a) $32; (b) $192
