Elijah and Dylan went shopping with a total amount of $300. They had $250 left after shopping. Elijah's remaining money was 4 times the amount he paid for. Dylan's remaining money was 6 times the amount he had spent.
- How much did Dylan spend?
- How much did Dylan bring along for shopping?
|
Elijah |
Dylan |
Total |
Before |
5 u |
7 p |
300 |
Change |
- 1 u |
- 1 p |
- 50 |
After |
4 u |
6 p |
250 |
(a)
Amount that Elijah and Dylan spent
= 300 - 250
= $50
Amount that Elijah and Dylan spent
= 1 u + 1 p
1 u + 1 p = 50
1 u = 50 - 1 p --- (1)
Amount that Elijah and Dylan had left
= 4 u + 6 p
4 u + 6 p = 250
4 u = 250 - 6 p --- (2)
Make u the same.
(1)
x 4 4 u = 200 - 4 p --- (3)
(3) = (2)
200 - 4 p = 250 - 6 p
6 p - 4 p = 250 - 200
2 p = 50
1 p = 50 ÷ 2 = 25
Amount that Dylan spent = $25
(b)
Amount that Dylan brought along
= 7 p
= 7 x 25
= $175
Answer(s): (a) $25; (b) $175