If Hilda gives Bryan $22, the amount of money she has will be 10% of his. If Bryan gives Hilda $68, he will have the same amount of money as her. How much money did each of them have?
(a) Bryan
(b) Hilda
|
Case 1 |
Case 2 |
|
Bryan |
Hilda |
Bryan |
Hilda |
Before |
10 u - 22 |
1 u + 22 |
5.5 u + 68 |
5.5 u - 68 |
Change |
+ 22 |
- 22 |
- 68 |
+ 68 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Hilda gives to Bryan, there is an internal transfer of money from Hilda to Bryan. The total amount that both have remains the same.
In Case 2, when Bryan gives to Hilda, there is an internal transfer of money from Bryan to Hilda. 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 Hilda and Bryan have
= 10 u + 1 u
= 11 u
Amount that Hilda and Bryan each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Bryan has at first is the same in Case 1 and Case 2.
10 u - 22 = 5.5 u + 68
10 u - 5.5 u = 68 + 22
4.5 u = 90
1 u = 90 ÷ 4.5 = 20
Amount that Bryan has
= 10 u - 22
= 10 x 20 - 22
= 200 - 22
= $178
(b)
Amount that Hilda has
= 1 u + 22
= 1 x 20 + 22
= 20 + 22
= $42
Answer(s): (a) $178; (b) $42