PSLEDana and Kathy went shopping together with a total amount of $59.40. Dana spent 2 times as much as Kathy. The amount Kathy had left was $9 more than what she had spent. She had 2 times as much money left as Dana.
(a) How much money did Kathy spend?
(b) How much money did Dana have at first?
|
Dana |
Kathy |
Total |
Before |
2.5 u + 4.5 |
2 u + 9 |
59.40 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 4.5 |
1 u + 9 |
|
(a)
Total amount that Dana and Kathy had at first
= (2.5 u + 4.5) + (2 u + 9)
= 2.5 u + 2 u + 4.5 + 9
= 4.5 u + 13.5
4.5 u + 13.5 = 59.4
4.5 u = 59.4 - 13.5
4.5 u = 45.9
1 u = 45.9 ÷ 4.5 = 10.2
Amount that Kathy had at first
= 1 u
= $10.20
(b)
Amount that Dana had at first
= 2.5 u + 4.5
= (2.5 x 10.2) + 4.5
= 25.5 + 4.5
= $30
Answer(s): (a) $10.20; (b) $30