Michael and Winnie has some money each. If Winnie gives Michael $11, he will have 7 times as much money as her. If Michael gives Winnie $16, he will have the same amount of money as her. How much money does each person have respectively?
- Michael?
- Winnie?
|
Case 1 |
Case 2 |
|
Michael |
Winnie |
Michael |
Winnie |
Before |
7 u - 11 |
1 u + 11 |
4 u + 16 |
4 u - 16 |
Change |
+ 11 |
- 11 |
- 16 |
+ 16 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Winnie gives Michael some money or Michael gives Winnie some money, the total amount of money remains the same.
Total amount that Michael and Winnie have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Michael and Winnie each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Michael has at first in Case 1 and Case 2 is the same.
7 u - 11 = 4 u + 16
7 u - 4 u = 16 + 11
1 u = 27
Amount that Michael has
= 4 u + 16
= 4 x 27 + 16
= 108 + 16
= $124
(b)
Amount that Winnie has
= 1 u + 11
= 27 + 11
= $38
Answer(s): (a) $124; (b) $38