If Zara gives Billy $24, the amount of money she has will be 40% of his. If Billy gives Zara $6, he will have the same amount of money as her. How much money did each of them have?
(a) Billy
(b) Zara
|
Case 1 |
Case 2 |
|
Billy |
Zara |
Billy |
Zara |
Before |
5 u - 24 |
2 u + 24 |
3.5 u + 6 |
3.5 u - 6 |
Change |
+ 24 |
- 24 |
- 6 |
+ 6 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Zara gives to Billy, there is an internal transfer of money from Zara to Billy. The total amount that both have remains the same.
In Case 2, when Billy gives to Zara, there is an internal transfer of money from Billy to Zara. 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 Zara and Billy have
= 5 u + 2 u
= 7 u
Amount that Zara 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 + 6
5 u - 3.5 u = 6 + 24
1.5 u = 30
1 u = 30 ÷ 1.5 = 20
Amount that Billy has
= 5 u - 24
= 5 x 20 - 24
= 100 - 24
= $76
(b)
Amount that Zara has
= 2 u + 24
= 2 x 20 + 24
= 40 + 24
= $64
Answer(s): (a) $76; (b) $64