If Erika gives Cole $26, the amount of money she has will be 40% of his. If Cole gives Erika $19, he will have the same amount of money as her. How much money did each of them have?
(a) Cole
(b) Erika
|
Case 1 |
Case 2 |
|
Cole |
Erika |
Cole |
Erika |
Before |
5 u - 26 |
2 u + 26 |
3.5 u + 19 |
3.5 u - 19 |
Change |
+ 26 |
- 26 |
- 19 |
+ 19 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Erika gives to Cole, there is an internal transfer of money from Erika to Cole. The total amount that both have remains the same.
In Case 2, when Cole gives to Erika, there is an internal transfer of money from Cole to Erika. 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 Erika and Cole have
= 5 u + 2 u
= 7 u
Amount that Erika and Cole each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Cole has at first is the same in Case 1 and Case 2.
5 u - 26 = 3.5 u + 19
5 u - 3.5 u = 19 + 26
1.5 u = 45
1 u = 45 ÷ 1.5 = 30
Amount that Cole has
= 5 u - 26
= 5 x 30 - 26
= 150 - 26
= $124
(b)
Amount that Erika has
= 2 u + 26
= 2 x 30 + 26
= 60 + 26
= $86
Answer(s): (a) $124; (b) $86