If Marion gives Japheth $20, the amount of money she has will be 10% of his. If Japheth gives Marion $88, he will have the same amount of money as her. How much money did each of them have?
(a) Japheth
(b) Marion
|
Case 1 |
Case 2 |
|
Japheth |
Marion |
Japheth |
Marion |
Before |
10 u - 20 |
1 u + 20 |
5.5 u + 88 |
5.5 u - 88 |
Change |
+ 20 |
- 20 |
- 88 |
+ 88 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Marion gives to Japheth, there is an internal transfer of money from Marion to Japheth. The total amount that both have remains the same.
In Case 2, when Japheth gives to Marion, there is an internal transfer of money from Japheth to Marion. 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 Marion and Japheth have
= 10 u + 1 u
= 11 u
Amount that Marion and Japheth each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Japheth has at first is the same in Case 1 and Case 2.
10 u - 20 = 5.5 u + 88
10 u - 5.5 u = 88 + 20
4.5 u = 108
1 u = 108 ÷ 4.5 = 24
Amount that Japheth has
= 10 u - 20
= 10 x 24 - 20
= 240 - 20
= $220
(b)
Amount that Marion has
= 1 u + 20
= 1 x 24 + 20
= 24 + 20
= $44
Answer(s): (a) $220; (b) $44