Cole and Irene has some money each. If Irene gives Cole $20, he will have 5 times as much money as her. If Cole gives Irene $11, he will have the same amount of money as her. How much money does each person have respectively?
- Cole?
- Irene?
|
Case 1 |
Case 2 |
|
Cole |
Irene |
Cole |
Irene |
Before |
5 u - 20 |
1 u + 20 |
3 u + 11 |
3 u - 11 |
Change |
+ 20 |
- 20 |
- 11 |
+ 11 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Irene gives Cole some money or Cole gives Irene some money, the total amount of money remains the same.
Total amount that Cole and Irene have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Cole and Irene each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Cole has at first in Case 1 and Case 2 is the same.
5 u - 20 = 3 u + 11
5 u - 3 u = 11 + 20
1 u = 31
Amount that Cole has
= 3 u + 11
= 3 x 31 + 11
= 93 + 11
= $104
(b)
Amount that Irene has
= 1 u + 20
= 31 + 20
= $51
Answer(s): (a) $104; (b) $51