The ratio of the amount of money Olivia had to the amount of money Tiffany had was 5 : 6. Olivia then gave
45 of her money to Tiffany. In the end, Tiffany returned $54 to Olivia and they both had the same amount of money. How much money did each girl have at the beginning?
- Tiffany
- Olivia
|
Olivia |
Tiffany |
Total |
Before |
5 u |
6 u |
11 u |
Change 1 |
- 4 u |
+ 4 u |
|
After 1 |
1 u |
10 u |
11 u |
Change 2 |
+ 54 |
- 54 |
|
After 2 |
1 u + 54 |
10 u - 54 |
|
Amount that Olivia and Tiffany each had in the end is the same.
10 u - 54 = 1 u + 54
10 u - 1 u = 54 + 54
9 u = 108
1 u = 108 ÷ 9 = 12
Amount that Olivia had at first
= 5 u
= 5 x 12
= $60
(b)
Amount that Tiffany had at first
= 6 u
= 6 x 12
= $72
Answer(s): (a) $60; (b) $72