Luke and Daniel went shopping with a total amount of $160. They had $128 left after shopping. Luke's remaining money was 3 times the amount he paid for. Daniel's remaining money was 5 times the amount he had spent.
- How much did Daniel spend?
- How much did Daniel bring along for shopping?
| |
Luke |
Daniel |
Total |
| Before |
4 u |
6 p |
160 |
| Change |
- 1 u |
- 1 p |
- 32 |
| After |
3 u |
5 p |
128 |
(a)
Amount that Luke and Daniel spent
= 160 - 128
= $32
Amount that Luke and Daniel spent
= 1 u + 1 p
1 u + 1 p = 32
1 u = 32 - 1 p --- (1)
Amount that Luke and Daniel had left
= 3 u + 5 p
3 u + 5 p = 128
3 u = 128 - 5 p --- (2)
Make u the same.
(1)
x 3 3 u = 96 - 3 p --- (3)
(3) = (2)
96 - 3 p = 128 - 5 p
5 p - 3 p = 128 - 96
2 p = 32
1 p = 32 ÷ 2 = 16
Amount that Daniel spent = $16
(b)
Amount that Daniel brought along
= 6 p
= 6 x 16
= $96
Answer(s): (a) $16; (b) $96
