Howard and Rael have some money. If Howard gives $206 to Rael, the ratio of their money will be 2 : 5. If Howard gives $560 to Rael, the ratio of their money will be 1: 4. How much does Howard have?
| |
Case 1 |
Case 2 |
| |
Howard |
Rael |
Howard |
Rael |
| Before |
10 u + $206 |
25 u - $206 |
7 u + $560 |
28 u - $560 |
| Change |
- $206 |
+ $206 |
- $560 |
+ $560 |
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 Howard has at first is the same in both cases.
10 u + 206 = 7 u + 560
10 u - 7 u = 560 - 206
3 u = 354
1 u = 354 ÷ 3 = 118
Amount that Howard has
= 10 u + 206
= 10 x 118 + 206
= 1180 + 206
= $1386
Answer(s): $1386
