Flynn and Shannon has some money each. If Shannon gives Flynn $20, he will have 5 times as much money as her. If Flynn gives Shannon $11, he will have the same amount of money as her. How much money does each person have respectively?
- Flynn?
- Shannon?
| |
Case 1 |
Case 2 |
| |
Flynn |
Shannon |
Flynn |
Shannon |
| Before |
5 u - 20 |
1 u + 20 |
3 u + 11 |
3 u - 11 |
| Change |
+ 20 |
- 20 |
- 11 |
+ 11 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Shannon gives Flynn some money or Flynn gives Shannon some money, the total amount of money remains the same.
Total amount that Flynn and Shannon have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Flynn and Shannon each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Flynn has at first in Case 1 and Case 2 is the same.
5 u - 20 = 3 u + 11
5 u - 3 u = 11 + 20
1 u = 31
Amount that Flynn has
= 3 u + 11
= 3 x 31 + 11
= 93 + 11
= $104
(b)
Amount that Shannon has
= 1 u + 20
= 31 + 20
= $51
Answer(s): (a) $104; (b) $51
