Tim and Linda has some money each. If Linda gives Tim $16, he will have 5 times as much money as her. If Tim gives Linda $13, he will have the same amount of money as her. How much money does each person have respectively?
- Tim?
- Linda?
| |
Case 1 |
Case 2 |
| |
Tim |
Linda |
Tim |
Linda |
| Before |
5 u - 16 |
1 u + 16 |
3 u + 13 |
3 u - 13 |
| Change |
+ 16 |
- 16 |
- 13 |
+ 13 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Linda gives Tim some money or Tim gives Linda some money, the total amount of money remains the same.
Total amount that Tim and Linda have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Tim and Linda each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Tim has at first in Case 1 and Case 2 is the same.
5 u - 16 = 3 u + 13
5 u - 3 u = 13 + 16
1 u = 29
Amount that Tim has
= 3 u + 13
= 3 x 29 + 13
= 87 + 13
= $100
(b)
Amount that Linda has
= 1 u + 16
= 29 + 16
= $45
Answer(s): (a) $100; (b) $45
