The ratio of the amount of money Olivia had to the amount of money Mary had was 5 : 6. Olivia then gave
45 of her money to Mary. In the end, Mary returned $63 to Olivia and they both had the same amount of money. How much money did each girl have at the beginning?
- Mary
- Olivia
|
Olivia |
Mary |
Total |
Before |
5 u |
6 u |
11 u |
Change 1 |
- 4 u |
+ 4 u |
|
After 1 |
1 u |
10 u |
11 u |
Change 2 |
+ 63 |
- 63 |
|
After 2 |
1 u + 63 |
10 u - 63 |
|
Amount that Olivia and Mary each had in the end is the same.
10 u - 63 = 1 u + 63
10 u - 1 u = 63 + 63
9 u = 126
1 u = 126 ÷ 9 = 14
Amount that Olivia had at first
= 5 u
= 5 x 14
= $70
(b)
Amount that Mary had at first
= 6 u
= 6 x 14
= $84
Answer(s): (a) $70; (b) $84