PSLEKylie and Cathy went shopping together with a total amount of $114.60. Kylie spent 2 times as much as Cathy. The amount Cathy had left was $17 more than what she had spent. She had 2 times as much money left as Kylie.
(a) How much money did Cathy spend?
(b) How much money did Kylie have at first?
|
Kylie |
Cathy |
Total |
Before |
2.5 u + 8.5 |
2 u + 17 |
114.60 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 8.5 |
1 u + 17 |
|
(a)
Total amount that Kylie and Cathy had at first
= (2.5 u + 8.5) + (2 u + 17)
= 2.5 u + 2 u + 8.5 + 17
= 4.5 u + 25.5
4.5 u + 25.5 = 114.6
4.5 u = 114.6 - 25.5
4.5 u = 89.1
1 u = 89.1 ÷ 4.5 = 19.8
Amount that Cathy had at first
= 1 u
= $19.80
(b)
Amount that Kylie had at first
= 2.5 u + 8.5
= (2.5 x 19.8) + 8.5
= 49.5 + 8.5
= $58
Answer(s): (a) $19.80; (b) $58