PSLEDiana and Fanny went shopping together with a total amount of $104.40. Diana spent 2 times as much as Fanny. The amount Fanny had left was $27 more than what she had spent. She had 2 times as much money left as Diana.
(a) How much money did Fanny spend?
(b) How much money did Diana have at first?
|
Diana |
Fanny |
Total |
Before |
2.5 u + 13.5 |
2 u + 27 |
104.40 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 13.5 |
1 u + 27 |
|
(a)
Total amount that Diana and Fanny had at first
= (2.5 u + 13.5) + (2 u + 27)
= 2.5 u + 2 u + 13.5 + 27
= 4.5 u + 40.5
4.5 u + 40.5 = 104.4
4.5 u = 104.4 - 40.5
4.5 u = 63.9
1 u = 63.9 ÷ 4.5 = 14.2
Amount that Fanny had at first
= 1 u
= $14.20
(b)
Amount that Diana had at first
= 2.5 u + 13.5
= (2.5 x 14.2) + 13.5
= 35.5 + 13.5
= $49
Answer(s): (a) $14.20; (b) $49