Mark and Rael went shopping with a total amount of $144. They had $120 left after shopping. Mark's remaining money was 3 times the amount he paid for. Rael's remaining money was 7 times the amount he had spent.
- How much did Rael spend?
- How much did Rael bring along for shopping?
| |
Mark |
Rael |
Total |
| Before |
4 u |
8 p |
144 |
| Change |
- 1 u |
- 1 p |
- 24 |
| After |
3 u |
7 p |
120 |
(a)
Amount that Mark and Rael spent
= 144 - 120
= $24
Amount that Mark and Rael spent
= 1 u + 1 p
1 u + 1 p = 24
1 u = 24 - 1 p --- (1)
Amount that Mark and Rael had left
= 3 u + 7 p
3 u + 7 p = 120
3 u = 120 - 7 p --- (2)
Make u the same.
(1)
x 3 3 u = 72 - 3 p --- (3)
(3) = (2)
72 - 3 p = 120 - 7 p
7 p - 3 p = 120 - 72
4 p = 48
1 p = 48 ÷ 4 = 12
Amount that Rael spent = $12
(b)
Amount that Rael brought along
= 8 p
= 8 x 12
= $96
Answer(s): (a) $12; (b) $96
