The ratio of the amount of money Gwen had to the amount of money Nicole had was 7 : 8. Gwen then gave
67 of her money to Nicole. In the end, Nicole returned $78 to Gwen and they both had the same amount of money. How much money did each girl have at the beginning?
- Nicole
- Gwen
|
Gwen |
Nicole |
Total |
Before |
7 u |
8 u |
15 u |
Change 1 |
- 6 u |
+ 6 u |
|
After 1 |
1 u |
14 u |
15 u |
Change 2 |
+ 78 |
- 78 |
|
After 2 |
1 u + 78 |
14 u - 78 |
|
Amount that Gwen and Nicole each had in the end is the same.
14 u - 78 = 1 u + 78
14 u - 1 u = 78 + 78
13 u = 156
1 u = 156 ÷ 13 = 12
Amount that Gwen had at first
= 7 u
= 7 x 12
= $84
(b)
Amount that Nicole had at first
= 8 u
= 8 x 12
= $96
Answer(s): (a) $84; (b) $96