Simon and Mary has some money each. If Mary gives Simon $16, he will have 7 times as much money as her. If Simon gives Mary $20, he will have the same amount of money as her. How much money does each person have respectively?
- Simon?
- Mary?
| |
Case 1 |
Case 2 |
| |
Simon |
Mary |
Simon |
Mary |
| Before |
7 u - 16 |
1 u + 16 |
4 u + 20 |
4 u - 20 |
| Change |
+ 16 |
- 16 |
- 20 |
+ 20 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Mary gives Simon some money or Simon gives Mary some money, the total amount of money remains the same.
Total amount that Simon and Mary have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Simon and Mary each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Simon has at first in Case 1 and Case 2 is the same.
7 u - 16 = 4 u + 20
7 u - 4 u = 20 + 16
1 u = 36
Amount that Simon has
= 4 u + 20
= 4 x 36 + 20
= 144 + 20
= $164
(b)
Amount that Mary has
= 1 u + 16
= 36 + 16
= $52
Answer(s): (a) $164; (b) $52
