If Tammy gives Bryan $23, the amount of money she has will be 40% of his. If Bryan gives Tammy $19, he will have the same amount of money as her. How much money did each of them have?
(a) Bryan
(b) Tammy
|
Case 1 |
Case 2 |
|
Bryan |
Tammy |
Bryan |
Tammy |
Before |
5 u - 23 |
2 u + 23 |
3.5 u + 19 |
3.5 u - 19 |
Change |
+ 23 |
- 23 |
- 19 |
+ 19 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Tammy gives to Bryan, there is an internal transfer of money from Tammy to Bryan. The total amount that both have remains the same.
In Case 2, when Bryan gives to Tammy, there is an internal transfer of money from Bryan to Tammy. 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 Tammy and Bryan have
= 5 u + 2 u
= 7 u
Amount that Tammy and Bryan each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Bryan has at first is the same in Case 1 and Case 2.
5 u - 23 = 3.5 u + 19
5 u - 3.5 u = 19 + 23
1.5 u = 42
1 u = 42 ÷ 1.5 = 28
Amount that Bryan has
= 5 u - 23
= 5 x 28 - 23
= 140 - 23
= $117
(b)
Amount that Tammy has
= 2 u + 23
= 2 x 28 + 23
= 56 + 23
= $79
Answer(s): (a) $117; (b) $79