Liam and Tammy has some money each. If Tammy gives Liam $16, he will have 7 times as much money as her. If Liam gives Tammy $17, he will have the same amount of money as her. How much money does each person have respectively?
- Liam?
- Tammy?
|
Case 1 |
Case 2 |
|
Liam |
Tammy |
Liam |
Tammy |
Before |
7 u - 16 |
1 u + 16 |
4 u + 17 |
4 u - 17 |
Change |
+ 16 |
- 16 |
- 17 |
+ 17 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Tammy gives Liam some money or Liam gives Tammy some money, the total amount of money remains the same.
Total amount that Liam and Tammy have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Liam and Tammy each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Liam has at first in Case 1 and Case 2 is the same.
7 u - 16 = 4 u + 17
7 u - 4 u = 17 + 16
1 u = 33
Amount that Liam has
= 4 u + 17
= 4 x 33 + 17
= 132 + 17
= $149
(b)
Amount that Tammy has
= 1 u + 16
= 33 + 16
= $49
Answer(s): (a) $149; (b) $49