Jeremy and Ian went shopping with a total amount of $100. They had $80 left after shopping. Jeremy's remaining money was 3 times the amount he paid for. Ian's remaining money was 5 times the amount he had spent.
- How much did Ian spend?
- How much did Ian bring along for shopping?
| |
Jeremy |
Ian |
Total |
| Before |
4 u |
6 p |
100 |
| Change |
- 1 u |
- 1 p |
- 20 |
| After |
3 u |
5 p |
80 |
(a)
Amount that Jeremy and Ian spent
= 100 - 80
= $20
Amount that Jeremy and Ian spent
= 1 u + 1 p
1 u + 1 p = 20
1 u = 20 - 1 p --- (1)
Amount that Jeremy and Ian had left
= 3 u + 5 p
3 u + 5 p = 80
3 u = 80 - 5 p --- (2)
Make u the same.
(1)
x 3 3 u = 60 - 3 p --- (3)
(3) = (2)
60 - 3 p = 80 - 5 p
5 p - 3 p = 80 - 60
2 p = 20
1 p = 20 ÷ 2 = 10
Amount that Ian spent = $10
(b)
Amount that Ian brought along
= 6 p
= 6 x 10
= $60
Answer(s): (a) $10; (b) $60
