If Nicole gives Rael $37, the amount of money she has will be 30% of his. If Rael gives Nicole $54, he will have the same amount of money as her. How much money did each of them have?
(a) Rael
(b) Nicole
|
Case 1 |
Case 2 |
|
Rael |
Nicole |
Rael |
Nicole |
Before |
10 u - 37 |
3 u + 37 |
6.5 u + 54 |
6.5 u - 54 |
Change |
+ 37 |
- 37 |
- 54 |
+ 54 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Nicole gives to Rael, there is an internal transfer of money from Nicole to Rael. The total amount that both have remains the same.
In Case 2, when Rael gives to Nicole, there is an internal transfer of money from Rael to Nicole. 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 Nicole and Rael have
= 10 u + 3 u
= 13 u
Amount that Nicole and Rael each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Rael has at first is the same in Case 1 and Case 2.
10 u - 37 = 6.5 u + 54
10 u - 6.5 u = 54 + 37
3.5 u = 91
1 u = 91 ÷ 3.5 = 26
Amount that Rael has
= 10 u - 37
= 10 x 26 - 37
= 260 - 37
= $223
(b)
Amount that Nicole has
= 3 u + 37
= 3 x 26 + 37
= 78 + 37
= $115
Answer(s): (a) $223; (b) $115