If Risa gives Brandon $35, the amount of money she has will be 30% of his. If Brandon gives Risa $133, he will have the same amount of money as her. How much money did each of them have?
(a) Brandon
(b) Risa
|
Case 1 |
Case 2 |
|
Brandon |
Risa |
Brandon |
Risa |
Before |
10 u - 35 |
3 u + 35 |
6.5 u + 133 |
6.5 u - 133 |
Change |
+ 35 |
- 35 |
- 133 |
+ 133 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Risa gives to Brandon, there is an internal transfer of money from Risa to Brandon. The total amount that both have remains the same.
In Case 2, when Brandon gives to Risa, there is an internal transfer of money from Brandon to Risa. 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 Risa and Brandon have
= 10 u + 3 u
= 13 u
Amount that Risa and Brandon each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Brandon has at first is the same in Case 1 and Case 2.
10 u - 35 = 6.5 u + 133
10 u - 6.5 u = 133 + 35
3.5 u = 168
1 u = 168 ÷ 3.5 = 48
Amount that Brandon has
= 10 u - 35
= 10 x 48 - 35
= 480 - 35
= $445
(b)
Amount that Risa has
= 3 u + 35
= 3 x 48 + 35
= 144 + 35
= $179
Answer(s): (a) $445; (b) $179