Pierre and Ken went shopping with a total amount of $490. They had $420 left after shopping. Pierre's remaining money was 5 times the amount he paid for. Ken's remaining money was 7 times the amount he had spent.
- How much did Ken spend?
- How much did Ken bring along for shopping?
| |
Pierre |
Ken |
Total |
| Before |
6 u |
8 p |
490 |
| Change |
- 1 u |
- 1 p |
- 70 |
| After |
5 u |
7 p |
420 |
(a)
Amount that Pierre and Ken spent
= 490 - 420
= $70
Amount that Pierre and Ken spent
= 1 u + 1 p
1 u + 1 p = 70
1 u = 70 - 1 p --- (1)
Amount that Pierre and Ken had left
= 5 u + 7 p
5 u + 7 p = 420
5 u = 420 - 7 p --- (2)
Make u the same.
(1)
x 5 5 u = 350 - 5 p --- (3)
(3) = (2)
350 - 5 p = 420 - 7 p
7 p - 5 p = 420 - 350
2 p = 70
1 p = 70 ÷ 2 = 35
Amount that Ken spent = $35
(b)
Amount that Ken brought along
= 8 p
= 8 x 35
= $280
Answer(s): (a) $35; (b) $280
