PSLEZoe and Rachel went shopping together with a total amount of $121.80. Zoe spent 2 times as much as Rachel. The amount Rachel had left was $29 more than what she had spent. She had 2 times as much money left as Zoe.
(a) How much money did Rachel spend?
(b) How much money did Zoe have at first?
|
Zoe |
Rachel |
Total |
Before |
2.5 u + 14.5 |
2 u + 29 |
121.80 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 14.5 |
1 u + 29 |
|
(a)
Total amount that Zoe and Rachel had at first
= (2.5 u + 14.5) + (2 u + 29)
= 2.5 u + 2 u + 14.5 + 29
= 4.5 u + 43.5
4.5 u + 43.5 = 121.8
4.5 u = 121.8 - 43.5
4.5 u = 78.3
1 u = 78.3 ÷ 4.5 = 17.4
Amount that Rachel had at first
= 1 u
= $17.40
(b)
Amount that Zoe had at first
= 2.5 u + 14.5
= (2.5 x 17.4) + 14.5
= 43.5 + 14.5
= $58
Answer(s): (a) $17.40; (b) $58