The ratio of the amount of money Marion had to the amount of money Xylia had was 7 : 8. Marion then gave
67 of her money to Xylia. In the end, Xylia returned $78 to Marion and they both had the same amount of money. How much money did each girl have at the beginning?
- Xylia
- Marion
|
Marion |
Xylia |
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 Marion and Xylia 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 Marion had at first
= 7 u
= 7 x 12
= $84
(b)
Amount that Xylia had at first
= 8 u
= 8 x 12
= $96
Answer(s): (a) $84; (b) $96