Ken and Rael went shopping with a total amount of $481. They had $407 left after shopping. Ken's remaining money was 4 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?
| |
Ken |
Rael |
Total |
| Before |
5 u |
8 p |
481 |
| Change |
- 1 u |
- 1 p |
- 74 |
| After |
4 u |
7 p |
407 |
(a)
Amount that Ken and Rael spent
= 481 - 407
= $74
Amount that Ken and Rael spent
= 1 u + 1 p
1 u + 1 p = 74
1 u = 74 - 1 p --- (1)
Amount that Ken and Rael had left
= 4 u + 7 p
4 u + 7 p = 407
4 u = 407 - 7 p --- (2)
Make u the same.
(1)
x 4 4 u = 296 - 4 p --- (3)
(3) = (2)
296 - 4 p = 407 - 7 p
7 p - 4 p = 407 - 296
3 p = 111
1 p = 111 ÷ 3 = 37
Amount that Rael spent = $37
(b)
Amount that Rael brought along
= 8 p
= 8 x 37
= $296
Answer(s): (a) $37; (b) $296
