Andy and Lynn has some money each. If Lynn gives Andy $15, he will have 5 times as much money as her. If Andy gives Lynn $18, he will have the same amount of money as her. How much money does each person have respectively?
- Andy?
- Lynn?
| |
Case 1 |
Case 2 |
| |
Andy |
Lynn |
Andy |
Lynn |
| Before |
5 u - 15 |
1 u + 15 |
3 u + 18 |
3 u - 18 |
| Change |
+ 15 |
- 15 |
- 18 |
+ 18 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Lynn gives Andy some money or Andy gives Lynn some money, the total amount of money remains the same.
Total amount that Andy and Lynn have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Andy and Lynn each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Andy has at first in Case 1 and Case 2 is the same.
5 u - 15 = 3 u + 18
5 u - 3 u = 18 + 15
1 u = 33
Amount that Andy has
= 3 u + 18
= 3 x 33 + 18
= 99 + 18
= $117
(b)
Amount that Lynn has
= 1 u + 15
= 33 + 15
= $48
Answer(s): (a) $117; (b) $48
