The ratio of the amount of money Mary had to the amount of money Esther had was 6 : 7. Mary then gave
56 of her money to Esther. In the end, Esther returned $44 to Mary and they both had the same amount of money. How much money did each girl have at the beginning?
- Esther
- Mary
|
Mary |
Esther |
Total |
Before |
6 u |
7 u |
13 u |
Change 1 |
- 5 u |
+ 5 u |
|
After 1 |
1 u |
12 u |
13 u |
Change 2 |
+ 44 |
- 44 |
|
After 2 |
1 u + 44 |
12 u - 44 |
|
Amount that Mary and Esther each had in the end is the same.
12 u - 44 = 1 u + 44
12 u - 1 u = 44 + 44
11 u = 88
1 u = 88 ÷ 11 = 8
Amount that Mary had at first
= 6 u
= 6 x 8
= $48
(b)
Amount that Esther had at first
= 7 u
= 7 x 8
= $56
Answer(s): (a) $48; (b) $56