If Yen gives Tommy $32, the amount of money she has will be 25% of his. If Tommy gives Yen $19, he will have the same amount of money as her. How much money did each of them have?
(a) Tommy
(b) Yen
|
Case 1 |
Case 2 |
|
Tommy |
Yen |
Tommy |
Yen |
Before |
4 u - 32 |
1 u + 32 |
2.5 u + 19 |
2.5 u - 19 |
Change |
+ 32 |
- 32 |
- 19 |
+ 19 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Yen gives to Tommy, there is an internal transfer of money from Yen to Tommy. The total amount that both have remains the same.
In Case 2, when Tommy gives to Yen, there is an internal transfer of money from Tommy to Yen. 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 Yen and Tommy have
= 4 u + 1 u
= 5 u
Amount that Yen and Tommy each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Tommy has at first is the same in Case 1 and Case 2.
4 u - 32 = 2.5 u + 19
4 u - 2.5 u = 19 + 32
1.5 u = 51
1 u = 51 ÷ 1.5 = 34
Amount that Tommy has
= 4 u - 32
= 4 x 34 - 32
= 136 - 32
= $104
(b)
Amount that Yen has
= 1 u + 32
= 1 x 34 + 32
= 34 + 32
= $66
Answer(s): (a) $104; (b) $66