Bobby and Betty has some money each. If Betty gives Bobby $16, he will have 5 times as much money as her. If Bobby gives Betty $17, he will have the same amount of money as her. How much money does each person have respectively?
- Bobby?
- Betty?
| |
Case 1 |
Case 2 |
| |
Bobby |
Betty |
Bobby |
Betty |
| Before |
5 u - 16 |
1 u + 16 |
3 u + 17 |
3 u - 17 |
| Change |
+ 16 |
- 16 |
- 17 |
+ 17 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Betty gives Bobby some money or Bobby gives Betty some money, the total amount of money remains the same.
Total amount that Bobby and Betty have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Bobby and Betty each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Bobby has at first in Case 1 and Case 2 is the same.
5 u - 16 = 3 u + 17
5 u - 3 u = 17 + 16
1 u = 33
Amount that Bobby has
= 3 u + 17
= 3 x 33 + 17
= 99 + 17
= $116
(b)
Amount that Betty has
= 1 u + 16
= 33 + 16
= $49
Answer(s): (a) $116; (b) $49
