If Joelle gives Brandon $16, the amount of money she has will be 25% of his. If Brandon gives Joelle $35, he will have the same amount of money as her. How much money did each of them have?
(a) Brandon
(b) Joelle
|
Case 1 |
Case 2 |
|
Brandon |
Joelle |
Brandon |
Joelle |
Before |
4 u - 16 |
1 u + 16 |
2.5 u + 35 |
2.5 u - 35 |
Change |
+ 16 |
- 16 |
- 35 |
+ 35 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Joelle gives to Brandon, there is an internal transfer of money from Joelle to Brandon. The total amount that both have remains the same.
In Case 2, when Brandon gives to Joelle, there is an internal transfer of money from Brandon to Joelle. 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 Joelle and Brandon have
= 4 u + 1 u
= 5 u
Amount that Joelle and Brandon each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Brandon has at first is the same in Case 1 and Case 2.
4 u - 16 = 2.5 u + 35
4 u - 2.5 u = 35 + 16
1.5 u = 51
1 u = 51 ÷ 1.5 = 34
Amount that Brandon has
= 4 u - 16
= 4 x 34 - 16
= 136 - 16
= $120
(b)
Amount that Joelle has
= 1 u + 16
= 1 x 34 + 16
= 34 + 16
= $50
Answer(s): (a) $120; (b) $50