Tommy and Winnie has some money each. If Winnie gives Tommy $11, he will have 7 times as much money as her. If Tommy gives Winnie $15, he will have the same amount of money as her. How much money does each person have respectively?
- Tommy?
- Winnie?
|
Case 1 |
Case 2 |
|
Tommy |
Winnie |
Tommy |
Winnie |
Before |
7 u - 11 |
1 u + 11 |
4 u + 15 |
4 u - 15 |
Change |
+ 11 |
- 11 |
- 15 |
+ 15 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Winnie gives Tommy some money or Tommy gives Winnie some money, the total amount of money remains the same.
Total amount that Tommy and Winnie have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Tommy and Winnie each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Tommy has at first in Case 1 and Case 2 is the same.
7 u - 11 = 4 u + 15
7 u - 4 u = 15 + 11
1 u = 26
Amount that Tommy has
= 4 u + 15
= 4 x 26 + 15
= 104 + 15
= $119
(b)
Amount that Winnie has
= 1 u + 11
= 26 + 11
= $37
Answer(s): (a) $119; (b) $37