If Opal gives Vaidev $36, the amount of money she has will be 30% of his. If Vaidev gives Opal $83, he will have the same amount of money as her. How much money did each of them have?
(a) Vaidev
(b) Opal
|
Case 1 |
Case 2 |
|
Vaidev |
Opal |
Vaidev |
Opal |
Before |
10 u - 36 |
3 u + 36 |
6.5 u + 83 |
6.5 u - 83 |
Change |
+ 36 |
- 36 |
- 83 |
+ 83 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Opal gives to Vaidev, there is an internal transfer of money from Opal to Vaidev. The total amount that both have remains the same.
In Case 2, when Vaidev gives to Opal, there is an internal transfer of money from Vaidev 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 Vaidev have
= 10 u + 3 u
= 13 u
Amount that Opal and Vaidev each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Vaidev has at first is the same in Case 1 and Case 2.
10 u - 36 = 6.5 u + 83
10 u - 6.5 u = 83 + 36
3.5 u = 119
1 u = 119 ÷ 3.5 = 34
Amount that Vaidev has
= 10 u - 36
= 10 x 34 - 36
= 340 - 36
= $304
(b)
Amount that Opal has
= 3 u + 36
= 3 x 34 + 36
= 102 + 36
= $138
Answer(s): (a) $304; (b) $138