If Sabrina gives Billy $24, the amount of money she has will be 40% of his. If Billy gives Sabrina $9, he will have the same amount of money as her. How much money did each of them have?
(a) Billy
(b) Sabrina
|
Case 1 |
Case 2 |
|
Billy |
Sabrina |
Billy |
Sabrina |
Before |
5 u - 24 |
2 u + 24 |
3.5 u + 9 |
3.5 u - 9 |
Change |
+ 24 |
- 24 |
- 9 |
+ 9 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Sabrina gives to Billy, there is an internal transfer of money from Sabrina to Billy. The total amount that both have remains the same.
In Case 2, when Billy gives to Sabrina, there is an internal transfer of money from Billy to Sabrina. 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 Sabrina and Billy have
= 5 u + 2 u
= 7 u
Amount that Sabrina and Billy each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Billy has at first is the same in Case 1 and Case 2.
5 u - 24 = 3.5 u + 9
5 u - 3.5 u = 9 + 24
1.5 u = 33
1 u = 33 ÷ 1.5 = 22
Amount that Billy has
= 5 u - 24
= 5 x 22 - 24
= 110 - 24
= $86
(b)
Amount that Sabrina has
= 2 u + 24
= 2 x 22 + 24
= 44 + 24
= $68
Answer(s): (a) $86; (b) $68