PSLEEmma and Winnie went shopping together with a total amount of $100.20. Emma spent 2 times as much as Winnie. The amount Winnie had left was $17 more than what she had spent. She had 2 times as much money left as Emma.
(a) How much money did Winnie spend?
(b) How much money did Emma have at first?
|
Emma |
Winnie |
Total |
Before |
2.5 u + 8.5 |
2 u + 17 |
100.20 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 8.5 |
1 u + 17 |
|
(a)
Total amount that Emma and Winnie had at first
= (2.5 u + 8.5) + (2 u + 17)
= 2.5 u + 2 u + 8.5 + 17
= 4.5 u + 25.5
4.5 u + 25.5 = 100.2
4.5 u = 100.2 - 25.5
4.5 u = 74.7
1 u = 74.7 ÷ 4.5 = 16.6
Amount that Winnie had at first
= 1 u
= $16.60
(b)
Amount that Emma had at first
= 2.5 u + 8.5
= (2.5 x 16.6) + 8.5
= 41.5 + 8.5
= $50
Answer(s): (a) $16.60; (b) $50