David and Billy went shopping with a total amount of $240. They had $200 left after shopping. David's remaining money was 3 times the amount he paid for. Billy's remaining money was 7 times the amount he had spent.
- How much did Billy spend?
- How much did Billy bring along for shopping?
| |
David |
Billy |
Total |
| Before |
4 u |
8 p |
240 |
| Change |
- 1 u |
- 1 p |
- 40 |
| After |
3 u |
7 p |
200 |
(a)
Amount that David and Billy spent
= 240 - 200
= $40
Amount that David and Billy spent
= 1 u + 1 p
1 u + 1 p = 40
1 u = 40 - 1 p --- (1)
Amount that David and Billy had left
= 3 u + 7 p
3 u + 7 p = 200
3 u = 200 - 7 p --- (2)
Make u the same.
(1)
x 3 3 u = 120 - 3 p --- (3)
(3) = (2)
120 - 3 p = 200 - 7 p
7 p - 3 p = 200 - 120
4 p = 80
1 p = 80 ÷ 4 = 20
Amount that Billy spent = $20
(b)
Amount that Billy brought along
= 8 p
= 8 x 20
= $160
Answer(s): (a) $20; (b) $160
