If Risa gives Tim $34, the amount of money she has will be 30% of his. If Tim gives Risa $99, he will have the same amount of money as her. How much money did each of them have?
(a) Tim
(b) Risa
|
Case 1 |
Case 2 |
|
Tim |
Risa |
Tim |
Risa |
Before |
10 u - 34 |
3 u + 34 |
6.5 u + 99 |
6.5 u - 99 |
Change |
+ 34 |
- 34 |
- 99 |
+ 99 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Risa gives to Tim, there is an internal transfer of money from Risa to Tim. The total amount that both have remains the same.
In Case 2, when Tim gives to Risa, there is an internal transfer of money from Tim 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 Tim have
= 10 u + 3 u
= 13 u
Amount that Risa and Tim each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Tim has at first is the same in Case 1 and Case 2.
10 u - 34 = 6.5 u + 99
10 u - 6.5 u = 99 + 34
3.5 u = 133
1 u = 133 ÷ 3.5 = 38
Amount that Tim has
= 10 u - 34
= 10 x 38 - 34
= 380 - 34
= $346
(b)
Amount that Risa has
= 3 u + 34
= 3 x 38 + 34
= 114 + 34
= $148
Answer(s): (a) $346; (b) $148