PSLEYen and Rachel went shopping together with a total amount of $115.20. Yen spent 2 times as much as Rachel. The amount Rachel had left was $18 more than what she had spent. She had 2 times as much money left as Yen.
(a) How much money did Rachel spend?
(b) How much money did Yen have at first?
|
Yen |
Rachel |
Total |
Before |
2.5 u + 9 |
2 u + 18 |
115.20 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 9 |
1 u + 18 |
|
(a)
Total amount that Yen and Rachel had at first
= (2.5 u + 9) + (2 u + 18)
= 2.5 u + 2 u + 9 + 18
= 4.5 u + 27
4.5 u + 27 = 115.2
4.5 u = 115.2 - 27
4.5 u = 88.2
1 u = 88.2 ÷ 4.5 = 19.6
Amount that Rachel had at first
= 1 u
= $19.60
(b)
Amount that Yen had at first
= 2.5 u + 9
= (2.5 x 19.6) + 9
= 49 + 9
= $58
Answer(s): (a) $19.60; (b) $58