PSLEDiana and Gillian went shopping together with a total amount of $119.40. Diana spent 2 times as much as Gillian. The amount Gillian had left was $25 more than what she had spent. She had 2 times as much money left as Diana.
(a) How much money did Gillian spend?
(b) How much money did Diana have at first?
|
Diana |
Gillian |
Total |
Before |
2.5 u + 12.5 |
2 u + 25 |
119.40 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 12.5 |
1 u + 25 |
|
(a)
Total amount that Diana and Gillian had at first
= (2.5 u + 12.5) + (2 u + 25)
= 2.5 u + 2 u + 12.5 + 25
= 4.5 u + 37.5
4.5 u + 37.5 = 119.4
4.5 u = 119.4 - 37.5
4.5 u = 81.9
1 u = 81.9 ÷ 4.5 = 18.2
Amount that Gillian had at first
= 1 u
= $18.20
(b)
Amount that Diana had at first
= 2.5 u + 12.5
= (2.5 x 18.2) + 12.5
= 45.5 + 12.5
= $58
Answer(s): (a) $18.20; (b) $58