PSLEGwen and Esther went shopping together with a total amount of $108.60. Gwen spent 2 times as much as Esther. The amount Esther had left was $19 more than what she had spent. She had 2 times as much money left as Gwen.
(a) How much money did Esther spend?
(b) How much money did Gwen have at first?
|
Gwen |
Esther |
Total |
Before |
2.5 u + 9.5 |
2 u + 19 |
108.60 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 9.5 |
1 u + 19 |
|
(a)
Total amount that Gwen and Esther had at first
= (2.5 u + 9.5) + (2 u + 19)
= 2.5 u + 2 u + 9.5 + 19
= 4.5 u + 28.5
4.5 u + 28.5 = 108.6
4.5 u = 108.6 - 28.5
4.5 u = 80.1
1 u = 80.1 ÷ 4.5 = 17.8
Amount that Esther had at first
= 1 u
= $17.80
(b)
Amount that Gwen had at first
= 2.5 u + 9.5
= (2.5 x 17.8) + 9.5
= 44.5 + 9.5
= $54
Answer(s): (a) $17.80; (b) $54