If Xandra gives Tim $29, the amount of money she has will be 25% of his. If Tim gives Xandra $16, he will have the same amount of money as her. How much money did each of them have?
(a) Tim
(b) Xandra
|
Case 1 |
Case 2 |
|
Tim |
Xandra |
Tim |
Xandra |
Before |
4 u - 29 |
1 u + 29 |
2.5 u + 16 |
2.5 u - 16 |
Change |
+ 29 |
- 29 |
- 16 |
+ 16 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Xandra gives to Tim, there is an internal transfer of money from Xandra to Tim. The total amount that both have remains the same.
In Case 2, when Tim gives to Xandra, there is an internal transfer of money from Tim to Xandra. 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 Xandra and Tim have
= 4 u + 1 u
= 5 u
Amount that Xandra and Tim each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Tim has at first is the same in Case 1 and Case 2.
4 u - 29 = 2.5 u + 16
4 u - 2.5 u = 16 + 29
1.5 u = 45
1 u = 45 ÷ 1.5 = 30
Amount that Tim has
= 4 u - 29
= 4 x 30 - 29
= 120 - 29
= $91
(b)
Amount that Xandra has
= 1 u + 29
= 1 x 30 + 29
= 30 + 29
= $59
Answer(s): (a) $91; (b) $59