Jeremy and George went shopping with a total amount of $120. They had $96 left after shopping. Jeremy's remaining money was 3 times the amount he paid for. George's remaining money was 5 times the amount he had spent.
- How much did George spend?
- How much did George bring along for shopping?
|
Jeremy |
George |
Total |
Before |
4 u |
6 p |
120 |
Change |
- 1 u |
- 1 p |
- 24 |
After |
3 u |
5 p |
96 |
(a)
Amount that Jeremy and George spent
= 120 - 96
= $24
Amount that Jeremy and George spent
= 1 u + 1 p
1 u + 1 p = 24
1 u = 24 - 1 p --- (1)
Amount that Jeremy and George had left
= 3 u + 5 p
3 u + 5 p = 96
3 u = 96 - 5 p --- (2)
Make u the same.
(1)
x 3 3 u = 72 - 3 p --- (3)
(3) = (2)
72 - 3 p = 96 - 5 p
5 p - 3 p = 96 - 72
2 p = 24
1 p = 24 ÷ 2 = 12
Amount that George spent = $12
(b)
Amount that George brought along
= 6 p
= 6 x 12
= $72
Answer(s): (a) $12; (b) $72