SOLUTION: total of three numbers is 174. If the ratio between 1st and 3rd number is 1:4. And the ratio between 2nd and 3rd number is 9:16. Then what is the 2nd number?

Question 525559: total of three numbers is 174. If the ratio between 1st and 3rd number is 1:4. And the ratio between 2nd and 3rd number is 9:16. Then what is the 2nd number?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write an equation for each statement. Simplify each equation as much as you can.
We want to get a & b in terms of a.
:
total of three numbers is 174.
a + b + c = 174
:
If the ratio between 1st and 3rd number is 1:4.
=
Cross multiply
c = 4a
:
And the ratio between 2nd and 3rd number is 9:16.
=
Cross multiply
16b = 9c
replace c with 4a
16b = 9(4a)
16b = 36a
Divide both sides by 16
b = a
Reduce fraction
b = a
:
Substitute in the 1st equation
a + a + 4a = 174
multiply by 4 to get rid of denominators:
4a + 9a + 4(4a) = 4(174)
4a + 9a + 16a = 696
29a = 696
a =
a = 24 is the 1st number
Find the 2nd number
b = (24)
b = 9*6
b = 54 is the 2nd number, which is what they want here
:
:
Find the 3rd number to check the solutions in the 1st equation
c =4(24)
c = 96
24 + 54 + 96 = 174, confirms our solutions
:

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