Xavier and Liam went shopping with a total amount of $110. They had $88 left after shopping. Xavier's remaining money was 3 times the amount he paid for. Liam's remaining money was 5 times the amount he had spent.
- How much did Liam spend?
- How much did Liam bring along for shopping?
| |
Xavier |
Liam |
Total |
| Before |
4 u |
6 p |
110 |
| Change |
- 1 u |
- 1 p |
- 22 |
| After |
3 u |
5 p |
88 |
(a)
Amount that Xavier and Liam spent
= 110 - 88
= $22
Amount that Xavier and Liam spent
= 1 u + 1 p
1 u + 1 p = 22
1 u = 22 - 1 p --- (1)
Amount that Xavier and Liam had left
= 3 u + 5 p
3 u + 5 p = 88
3 u = 88 - 5 p --- (2)
Make u the same.
(1)
x 3 3 u = 66 - 3 p --- (3)
(3) = (2)
66 - 3 p = 88 - 5 p
5 p - 3 p = 88 - 66
2 p = 22
1 p = 22 ÷ 2 = 11
Amount that Liam spent = $11
(b)
Amount that Liam brought along
= 6 p
= 6 x 11
= $66
Answer(s): (a) $11; (b) $66
