If Abi gives Gabriel $39, the amount of money she has will be 10% of his. If Gabriel gives Abi $78, he will have the same amount of money as her. How much money did each of them have?
(a) Gabriel
(b) Abi
|
Case 1 |
Case 2 |
|
Gabriel |
Abi |
Gabriel |
Abi |
Before |
10 u - 39 |
1 u + 39 |
5.5 u + 78 |
5.5 u - 78 |
Change |
+ 39 |
- 39 |
- 78 |
+ 78 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Abi gives to Gabriel, there is an internal transfer of money from Abi to Gabriel. The total amount that both have remains the same.
In Case 2, when Gabriel gives to Abi, there is an internal transfer of money from Gabriel to Abi. The total amount that both have remains the same.
The total amount that both have in Case 1 and Case 2 are the same.
Total amount that Abi and Gabriel have
= 10 u + 1 u
= 11 u
Amount that Abi and Gabriel each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Gabriel has at first is the same in Case 1 and Case 2.
10 u - 39 = 5.5 u + 78
10 u - 5.5 u = 78 + 39
4.5 u = 117
1 u = 117 ÷ 4.5 = 26
Amount that Gabriel has
= 10 u - 39
= 10 x 26 - 39
= 260 - 39
= $221
(b)
Amount that Abi has
= 1 u + 39
= 1 x 26 + 39
= 26 + 39
= $65
Answer(s): (a) $221; (b) $65