Ahmad and Mary has some money each. If Mary gives Ahmad $18, he will have 3 times as much money as her. If Ahmad gives Mary $10, he will have the same amount of money as her. How much money does each person have respectively?
- Ahmad?
- Mary?
| |
Case 1 |
Case 2 |
| |
Ahmad |
Mary |
Ahmad |
Mary |
| Before |
3 u - 18 |
1 u + 18 |
2 u + 10 |
2 u - 10 |
| Change |
+ 18 |
- 18 |
- 10 |
+ 10 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Mary gives Ahmad some money or Ahmad gives Mary some money, the total amount of money remains the same.
Total amount that Ahmad and Mary have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Ahmad and Mary 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 - 18 = 2 u + 10
3 u - 2 u = 10 + 18
1 u = 28
Amount that Ahmad has
= 2 u + 10
= 2 x 28 + 10
= 56 + 10
= $66
(b)
Amount that Mary has
= 1 u + 18
= 28 + 18
= $46
Answer(s): (a) $66; (b) $46
