Tim and Elyse has some money each. If Elyse gives Tim $12, he will have 3 times as much money as her. If Tim gives Elyse $20, he will have the same amount of money as her. How much money does each person have respectively?
- Tim?
- Elyse?
| |
Case 1 |
Case 2 |
| |
Tim |
Elyse |
Tim |
Elyse |
| Before |
3 u - 12 |
1 u + 12 |
2 u + 20 |
2 u - 20 |
| Change |
+ 12 |
- 12 |
- 20 |
+ 20 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Elyse gives Tim some money or Tim gives Elyse some money, the total amount of money remains the same.
Total amount that Tim and Elyse have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Tim and Elyse each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Tim has at first in Case 1 and Case 2 is the same.
3 u - 12 = 2 u + 20
3 u - 2 u = 20 + 12
1 u = 32
Amount that Tim has
= 2 u + 20
= 2 x 32 + 20
= 64 + 20
= $84
(b)
Amount that Elyse has
= 1 u + 12
= 32 + 12
= $44
Answer(s): (a) $84; (b) $44
