If Mary gives Ryan $32, the amount of money she has will be 30% of his. If Ryan gives Mary $108, he will have the same amount of money as her. How much money did each of them have?
(a) Ryan
(b) Mary
|
Case 1 |
Case 2 |
|
Ryan |
Mary |
Ryan |
Mary |
Before |
10 u - 32 |
3 u + 32 |
6.5 u + 108 |
6.5 u - 108 |
Change |
+ 32 |
- 32 |
- 108 |
+ 108 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Mary gives to Ryan, there is an internal transfer of money from Mary to Ryan. The total amount that both have remains the same.
In Case 2, when Ryan gives to Mary, there is an internal transfer of money from Ryan to Mary. 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 Mary and Ryan have
= 10 u + 3 u
= 13 u
Amount that Mary and Ryan each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Ryan has at first is the same in Case 1 and Case 2.
10 u - 32 = 6.5 u + 108
10 u - 6.5 u = 108 + 32
3.5 u = 140
1 u = 140 ÷ 3.5 = 40
Amount that Ryan has
= 10 u - 32
= 10 x 40 - 32
= 400 - 32
= $368
(b)
Amount that Mary has
= 3 u + 32
= 3 x 40 + 32
= 120 + 32
= $152
Answer(s): (a) $368; (b) $152