The ratio of the amount of money Esther had to the amount of money Natalie had was 5 : 6. Esther then gave
45 of her money to Natalie. In the end, Natalie returned $72 to Esther and they both had the same amount of money. How much money did each girl have at the beginning?
- Natalie
- Esther
|
Esther |
Natalie |
Total |
Before |
5 u |
6 u |
11 u |
Change 1 |
- 4 u |
+ 4 u |
|
After 1 |
1 u |
10 u |
11 u |
Change 2 |
+ 72 |
- 72 |
|
After 2 |
1 u + 72 |
10 u - 72 |
|
Amount that Esther and Natalie each had in the end is the same.
10 u - 72 = 1 u + 72
10 u - 1 u = 72 + 72
9 u = 144
1 u = 144 ÷ 9 = 16
Amount that Esther had at first
= 5 u
= 5 x 16
= $80
(b)
Amount that Natalie had at first
= 6 u
= 6 x 16
= $96
Answer(s): (a) $80; (b) $96