If Gillian gives Sam $16, the amount of money she has will be 30% of his. If Sam gives Gillian $110, he will have the same amount of money as her. How much money did each of them have?
(a) Sam
(b) Gillian
|
Case 1 |
Case 2 |
|
Sam |
Gillian |
Sam |
Gillian |
Before |
10 u - 16 |
3 u + 16 |
6.5 u + 110 |
6.5 u - 110 |
Change |
+ 16 |
- 16 |
- 110 |
+ 110 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Gillian gives to Sam, there is an internal transfer of money from Gillian to Sam. The total amount that both have remains the same.
In Case 2, when Sam gives to Gillian, there is an internal transfer of money from Sam to Gillian. 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 Gillian and Sam have
= 10 u + 3 u
= 13 u
Amount that Gillian and Sam each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Sam has at first is the same in Case 1 and Case 2.
10 u - 16 = 6.5 u + 110
10 u - 6.5 u = 110 + 16
3.5 u = 126
1 u = 126 ÷ 3.5 = 36
Amount that Sam has
= 10 u - 16
= 10 x 36 - 16
= 360 - 16
= $344
(b)
Amount that Gillian has
= 3 u + 16
= 3 x 36 + 16
= 108 + 16
= $124
Answer(s): (a) $344; (b) $124