If Hazel gives Billy $31, the amount of money she has will be 10% of his. If Billy gives Hazel $122, he will have the same amount of money as her. How much money did each of them have?
(a) Billy
(b) Hazel
|
Case 1 |
Case 2 |
|
Billy |
Hazel |
Billy |
Hazel |
Before |
10 u - 31 |
1 u + 31 |
5.5 u + 122 |
5.5 u - 122 |
Change |
+ 31 |
- 31 |
- 122 |
+ 122 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Hazel gives to Billy, there is an internal transfer of money from Hazel to Billy. The total amount that both have remains the same.
In Case 2, when Billy gives to Hazel, there is an internal transfer of money from Billy to Hazel. 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 Hazel and Billy have
= 10 u + 1 u
= 11 u
Amount that Hazel and Billy each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Billy has at first is the same in Case 1 and Case 2.
10 u - 31 = 5.5 u + 122
10 u - 5.5 u = 122 + 31
4.5 u = 153
1 u = 153 ÷ 4.5 = 34
Amount that Billy has
= 10 u - 31
= 10 x 34 - 31
= 340 - 31
= $309
(b)
Amount that Hazel has
= 1 u + 31
= 1 x 34 + 31
= 34 + 31
= $65
Answer(s): (a) $309; (b) $65