If Hilda gives Sam $28, the amount of money she has will be 25% of his. If Sam gives Hilda $14, he will have the same amount of money as her. How much money did each of them have?
(a) Sam
(b) Hilda
|
Case 1 |
Case 2 |
|
Sam |
Hilda |
Sam |
Hilda |
Before |
4 u - 28 |
1 u + 28 |
2.5 u + 14 |
2.5 u - 14 |
Change |
+ 28 |
- 28 |
- 14 |
+ 14 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Hilda gives to Sam, there is an internal transfer of money from Hilda to Sam. The total amount that both have remains the same.
In Case 2, when Sam gives to Hilda, there is an internal transfer of money from Sam 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 Sam have
= 4 u + 1 u
= 5 u
Amount that Hilda and Sam each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Sam has at first is the same in Case 1 and Case 2.
4 u - 28 = 2.5 u + 14
4 u - 2.5 u = 14 + 28
1.5 u = 42
1 u = 42 ÷ 1.5 = 28
Amount that Sam has
= 4 u - 28
= 4 x 28 - 28
= 112 - 28
= $84
(b)
Amount that Hilda has
= 1 u + 28
= 1 x 28 + 28
= 28 + 28
= $56
Answer(s): (a) $84; (b) $56