If Elyse gives Glen $35, the amount of money she has will be 10% of his. If Glen gives Elyse $73, he will have the same amount of money as her. How much money did each of them have?
(a) Glen
(b) Elyse
|
Case 1 |
Case 2 |
|
Glen |
Elyse |
Glen |
Elyse |
Before |
10 u - 35 |
1 u + 35 |
5.5 u + 73 |
5.5 u - 73 |
Change |
+ 35 |
- 35 |
- 73 |
+ 73 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Elyse gives to Glen, there is an internal transfer of money from Elyse to Glen. The total amount that both have remains the same.
In Case 2, when Glen gives to Elyse, there is an internal transfer of money from Glen to Elyse. 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 Elyse and Glen have
= 10 u + 1 u
= 11 u
Amount that Elyse and Glen each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Glen has at first is the same in Case 1 and Case 2.
10 u - 35 = 5.5 u + 73
10 u - 5.5 u = 73 + 35
4.5 u = 108
1 u = 108 ÷ 4.5 = 24
Amount that Glen has
= 10 u - 35
= 10 x 24 - 35
= 240 - 35
= $205
(b)
Amount that Elyse has
= 1 u + 35
= 1 x 24 + 35
= 24 + 35
= $59
Answer(s): (a) $205; (b) $59