Elijah and Jack went shopping with a total amount of $340. They had $272 left after shopping. Elijah's remaining money was 3 times the amount he paid for. Jack's remaining money was 5 times the amount he had spent.
- How much did Jack spend?
- How much did Jack bring along for shopping?
| |
Elijah |
Jack |
Total |
| Before |
4 u |
6 p |
340 |
| Change |
- 1 u |
- 1 p |
- 68 |
| After |
3 u |
5 p |
272 |
(a)
Amount that Elijah and Jack spent
= 340 - 272
= $68
Amount that Elijah and Jack spent
= 1 u + 1 p
1 u + 1 p = 68
1 u = 68 - 1 p --- (1)
Amount that Elijah and Jack had left
= 3 u + 5 p
3 u + 5 p = 272
3 u = 272 - 5 p --- (2)
Make u the same.
(1)
x 3 3 u = 204 - 3 p --- (3)
(3) = (2)
204 - 3 p = 272 - 5 p
5 p - 3 p = 272 - 204
2 p = 68
1 p = 68 ÷ 2 = 34
Amount that Jack spent = $34
(b)
Amount that Jack brought along
= 6 p
= 6 x 34
= $204
Answer(s): (a) $34; (b) $204
