Bobby and Fanny has some money each. If Fanny gives Bobby $15, he will have 7 times as much money as her. If Bobby gives Fanny $11, he will have the same amount of money as her. How much money does each person have respectively?
- Bobby?
- Fanny?
| |
Case 1 |
Case 2 |
| |
Bobby |
Fanny |
Bobby |
Fanny |
| Before |
7 u - 15 |
1 u + 15 |
4 u + 11 |
4 u - 11 |
| Change |
+ 15 |
- 15 |
- 11 |
+ 11 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Fanny gives Bobby some money or Bobby gives Fanny some money, the total amount of money remains the same.
Total amount that Bobby and Fanny have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Bobby and Fanny each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Bobby has at first in Case 1 and Case 2 is the same.
7 u - 15 = 4 u + 11
7 u - 4 u = 11 + 15
1 u = 26
Amount that Bobby has
= 4 u + 11
= 4 x 26 + 11
= 104 + 11
= $115
(b)
Amount that Fanny has
= 1 u + 15
= 26 + 15
= $41
Answer(s): (a) $115; (b) $41
