If Opal gives Glen $37, the amount of money she has will be 30% of his. If Glen gives Opal $131, he will have the same amount of money as her. How much money did each of them have?
(a) Glen
(b) Opal
|
Case 1 |
Case 2 |
|
Glen |
Opal |
Glen |
Opal |
Before |
10 u - 37 |
3 u + 37 |
6.5 u + 131 |
6.5 u - 131 |
Change |
+ 37 |
- 37 |
- 131 |
+ 131 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Opal gives to Glen, there is an internal transfer of money from Opal to Glen. The total amount that both have remains the same.
In Case 2, when Glen gives to Opal, there is an internal transfer of money from Glen to Opal. 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 Opal and Glen have
= 10 u + 3 u
= 13 u
Amount that Opal and Glen each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Glen has at first is the same in Case 1 and Case 2.
10 u - 37 = 6.5 u + 131
10 u - 6.5 u = 131 + 37
3.5 u = 168
1 u = 168 ÷ 3.5 = 48
Amount that Glen has
= 10 u - 37
= 10 x 48 - 37
= 480 - 37
= $443
(b)
Amount that Opal has
= 3 u + 37
= 3 x 48 + 37
= 144 + 37
= $181
Answer(s): (a) $443; (b) $181