PSLEEmily and Elyse went shopping together with a total amount of $107.40. Emily spent 2 times as much as Elyse. The amount Elyse had left was $20 more than what she had spent. She had 2 times as much money left as Emily.
(a) How much money did Elyse spend?
(b) How much money did Emily have at first?
|
Emily |
Elyse |
Total |
Before |
2.5 u + 10 |
2 u + 20 |
107.40 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 10 |
1 u + 20 |
|
(a)
Total amount that Emily and Elyse had at first
= (2.5 u + 10) + (2 u + 20)
= 2.5 u + 2 u + 10 + 20
= 4.5 u + 30
4.5 u + 30 = 107.4
4.5 u = 107.4 - 30
4.5 u = 77.4
1 u = 77.4 ÷ 4.5 = 17.2
Amount that Elyse had at first
= 1 u
= $17.20
(b)
Amount that Emily had at first
= 2.5 u + 10
= (2.5 x 17.2) + 10
= 43 + 10
= $53
Answer(s): (a) $17.20; (b) $53