Bobby and Lynn has some money each. If Lynn gives Bobby $14, he will have 3 times as much money as her. If Bobby gives Lynn $15, he will have the same amount of money as her. How much money does each person have respectively?
- Bobby?
- Lynn?
| |
Case 1 |
Case 2 |
| |
Bobby |
Lynn |
Bobby |
Lynn |
| Before |
3 u - 14 |
1 u + 14 |
2 u + 15 |
2 u - 15 |
| Change |
+ 14 |
- 14 |
- 15 |
+ 15 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Lynn gives Bobby some money or Bobby gives Lynn some money, the total amount of money remains the same.
Total amount that Bobby and Lynn have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Bobby and Lynn each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Bobby has at first in Case 1 and Case 2 is the same.
3 u - 14 = 2 u + 15
3 u - 2 u = 15 + 14
1 u = 29
Amount that Bobby has
= 2 u + 15
= 2 x 29 + 15
= 58 + 15
= $73
(b)
Amount that Lynn has
= 1 u + 14
= 29 + 14
= $43
Answer(s): (a) $73; (b) $43
