If Opal gives Daniel $36, the amount of money she has will be 10% of his. If Daniel gives Opal $54, he will have the same amount of money as her. How much money did each of them have?
(a) Daniel
(b) Opal
|
Case 1 |
Case 2 |
|
Daniel |
Opal |
Daniel |
Opal |
Before |
10 u - 36 |
1 u + 36 |
5.5 u + 54 |
5.5 u - 54 |
Change |
+ 36 |
- 36 |
- 54 |
+ 54 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Opal gives to Daniel, there is an internal transfer of money from Opal to Daniel. The total amount that both have remains the same.
In Case 2, when Daniel gives to Opal, there is an internal transfer of money from Daniel 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 Daniel have
= 10 u + 1 u
= 11 u
Amount that Opal and Daniel each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Daniel has at first is the same in Case 1 and Case 2.
10 u - 36 = 5.5 u + 54
10 u - 5.5 u = 54 + 36
4.5 u = 90
1 u = 90 ÷ 4.5 = 20
Amount that Daniel has
= 10 u - 36
= 10 x 20 - 36
= 200 - 36
= $164
(b)
Amount that Opal has
= 1 u + 36
= 1 x 20 + 36
= 20 + 36
= $56
Answer(s): (a) $164; (b) $56