Ahmad and Shannon has some money each. If Shannon gives Ahmad $13, he will have 3 times as much money as her. If Ahmad gives Shannon $20, he will have the same amount of money as her. How much money does each person have respectively?
- Ahmad?
- Shannon?
| |
Case 1 |
Case 2 |
| |
Ahmad |
Shannon |
Ahmad |
Shannon |
| Before |
3 u - 13 |
1 u + 13 |
2 u + 20 |
2 u - 20 |
| Change |
+ 13 |
- 13 |
- 20 |
+ 20 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Shannon gives Ahmad some money or Ahmad gives Shannon some money, the total amount of money remains the same.
Total amount that Ahmad and Shannon have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Ahmad and Shannon each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Ahmad has at first in Case 1 and Case 2 is the same.
3 u - 13 = 2 u + 20
3 u - 2 u = 20 + 13
1 u = 33
Amount that Ahmad has
= 2 u + 20
= 2 x 33 + 20
= 66 + 20
= $86
(b)
Amount that Shannon has
= 1 u + 13
= 33 + 13
= $46
Answer(s): (a) $86; (b) $46
