PSLEDana and Esther went shopping together with a total amount of $87.60. Dana spent 2 times as much as Esther. The amount Esther had left was $14 more than what she had spent. She had 2 times as much money left as Dana.
(a) How much money did Esther spend?
(b) How much money did Dana have at first?
|
Dana |
Esther |
Total |
Before |
2.5 u + 7 |
2 u + 14 |
87.60 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 7 |
1 u + 14 |
|
(a)
Total amount that Dana and Esther had at first
= (2.5 u + 7) + (2 u + 14)
= 2.5 u + 2 u + 7 + 14
= 4.5 u + 21
4.5 u + 21 = 87.6
4.5 u = 87.6 - 21
4.5 u = 66.6
1 u = 66.6 ÷ 4.5 = 14.8
Amount that Esther had at first
= 1 u
= $14.80
(b)
Amount that Dana had at first
= 2.5 u + 7
= (2.5 x 14.8) + 7
= 37 + 7
= $44
Answer(s): (a) $14.80; (b) $44