PSLEIrene and Kathy went shopping together with a total amount of $77.40. Irene spent 2 times as much as Kathy. The amount Kathy had left was $12 more than what she had spent. She had 2 times as much money left as Irene.
(a) How much money did Kathy spend?
(b) How much money did Irene have at first?
|
Irene |
Kathy |
Total |
Before |
2.5 u + 6 |
2 u + 12 |
77.40 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 6 |
1 u + 12 |
|
(a)
Total amount that Irene and Kathy had at first
= (2.5 u + 6) + (2 u + 12)
= 2.5 u + 2 u + 6 + 12
= 4.5 u + 18
4.5 u + 18 = 77.4
4.5 u = 77.4 - 18
4.5 u = 59.4
1 u = 59.4 ÷ 4.5 = 13.2
Amount that Kathy had at first
= 1 u
= $13.20
(b)
Amount that Irene had at first
= 2.5 u + 6
= (2.5 x 13.2) + 6
= 33 + 6
= $39
Answer(s): (a) $13.20; (b) $39