SOLUTION: The sum of three numbers is 55. The ratio of the first to the second is 1:4, and the ratio of the second to the third is 2:3. Find three numbers.

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The sum of three numbers is 55. The ratio of the first to the second is 1:4, and the ratio of the second to the third is 2:3. Find three numbers.      Log On


   

Question 1049590: The sum of three numbers is 55. The ratio of the first to the second is 1:4, and the ratio of the second to the third is 2:3. Find three numbers.
Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
the main equations are
a%2Bb%2Bc=55
a%2Fb=1%2F4
b%2Fc=2%2F3

solution
b=4a first eq
12a=2c second eq
6a=c
c=6a second eq

a%2Bb%2Bc=55
a%2B4a%2B6a=55
11a=55
a=5
b=4a
b=4%2A5
b=20
6%2A5=c
30=c
the three numbers are a=5 b=20 and c=30
check
a%2Bb%2Bc=55
5%2B20%2B30=55
25%2B30=55
55=55

also
a%2Fb=1%2F4
b%2Fc=2%2F3

5%2F20=1%2F4
1%2F4=1%2F4
20%2F30=2%2F3
2%2F3=2%2F3
perfect