The ratio of the amount of money Opal had to the amount of money Natalie had was 6 : 7. Opal then gave
56 of her money to Natalie. In the end, Natalie returned $66 to Opal and they both had the same amount of money. How much money did each girl have at the beginning?
- Natalie
- Opal
|
Opal |
Natalie |
Total |
Before |
6 u |
7 u |
13 u |
Change 1 |
- 5 u |
+ 5 u |
|
After 1 |
1 u |
12 u |
13 u |
Change 2 |
+ 66 |
- 66 |
|
After 2 |
1 u + 66 |
12 u - 66 |
|
Amount that Opal and Natalie each had in the end is the same.
12 u - 66 = 1 u + 66
12 u - 1 u = 66 + 66
11 u = 132
1 u = 132 ÷ 11 = 12
Amount that Opal had at first
= 6 u
= 6 x 12
= $72
(b)
Amount that Natalie had at first
= 7 u
= 7 x 12
= $84
Answer(s): (a) $72; (b) $84