Andy and Shannon has some money each. If Shannon gives Andy $19, he will have 3 times as much money as her. If Andy gives Shannon $20, he will have the same amount of money as her. How much money does each person have respectively?
- Andy?
- Shannon?
|
Case 1 |
Case 2 |
|
Andy |
Shannon |
Andy |
Shannon |
Before |
3 u - 19 |
1 u + 19 |
2 u + 20 |
2 u - 20 |
Change |
+ 19 |
- 19 |
- 20 |
+ 20 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Shannon gives Andy some money or Andy gives Shannon some money, the total amount of money remains the same.
Total amount that Andy and Shannon have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Andy and Shannon each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Andy has at first in Case 1 and Case 2 is the same.
3 u - 19 = 2 u + 20
3 u - 2 u = 20 + 19
1 u = 39
Amount that Andy has
= 2 u + 20
= 2 x 39 + 20
= 78 + 20
= $98
(b)
Amount that Shannon has
= 1 u + 19
= 39 + 19
= $58
Answer(s): (a) $98; (b) $58