PSLEGem and Kimberly went shopping together with a total amount of $78.60. Gem spent 2 times as much as Kimberly. The amount Kimberly had left was $8 more than what she had spent. She had 2 times as much money left as Gem.
(a) How much money did Kimberly spend?
(b) How much money did Gem have at first?
|
Gem |
Kimberly |
Total |
Before |
2.5 u + 4 |
2 u + 8 |
78.60 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 4 |
1 u + 8 |
|
(a)
Total amount that Gem and Kimberly had at first
= (2.5 u + 4) + (2 u + 8)
= 2.5 u + 2 u + 4 + 8
= 4.5 u + 12
4.5 u + 12 = 78.6
4.5 u = 78.6 - 12
4.5 u = 66.6
1 u = 66.6 ÷ 4.5 = 14.8
Amount that Kimberly had at first
= 1 u
= $14.80
(b)
Amount that Gem had at first
= 2.5 u + 4
= (2.5 x 14.8) + 4
= 37 + 4
= $41
Answer(s): (a) $14.80; (b) $41