Tommy and Liam have some money. If Tommy gives $336 to Liam, the ratio of their money will be 2 : 5. If Tommy gives $663 to Liam, the ratio of their money will be 1: 4. How much does Tommy have?
| |
Case 1 |
Case 2 |
| |
Tommy |
Liam |
Tommy |
Liam |
| Before |
10 u + $336 |
25 u - $336 |
7 u + $663 |
28 u - $663 |
| Change |
- $336 |
+ $336 |
- $663 |
+ $663 |
After
|
2x5 =
10 u |
5x5 =
25 u |
1x7 =
7 u |
4x7 =
28 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 7 and 5 is 35.
The amount that Tommy has at first is the same in both cases.
10 u + 336 = 7 u + 663
10 u - 7 u = 663 - 336
3 u = 327
1 u = 327 ÷ 3 = 109
Amount that Tommy has
= 10 u + 336
= 10 x 109 + 336
= 1090 + 336
= $1426
Answer(s): $1426
