PSLEGwen and Emily went shopping together with a total amount of $90.60. Gwen spent 2 times as much as Emily. The amount Emily had left was $7 more than what she had spent. She had 2 times as much money left as Gwen.
(a) How much money did Emily spend?
(b) How much money did Gwen have at first?
|
Gwen |
Emily |
Total |
Before |
2.5 u + 3.5 |
2 u + 7 |
90.60 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 3.5 |
1 u + 7 |
|
(a)
Total amount that Gwen and Emily had at first
= (2.5 u + 3.5) + (2 u + 7)
= 2.5 u + 2 u + 3.5 + 7
= 4.5 u + 10.5
4.5 u + 10.5 = 90.6
4.5 u = 90.6 - 10.5
4.5 u = 80.1
1 u = 80.1 ÷ 4.5 = 17.8
Amount that Emily had at first
= 1 u
= $17.80
(b)
Amount that Gwen had at first
= 2.5 u + 3.5
= (2.5 x 17.8) + 3.5
= 44.5 + 3.5
= $48
Answer(s): (a) $17.80; (b) $48