The sum of three numbers is 174.The ratio of second number to the third number is 9:16 and the ratio of the first number to the third is 1:4.The second number is
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The second number is 54
Answer:
54
Step-by-step explanation:
total of three numbers is 174.
[a + b + c = 174]
If the ratio between 1st and 3rd number is 1:4.
a/c = 1/4
Cross multiply
[c = 4a]
And the ratio between 2nd and 3rd number is 9:16.
b/c = 9/16
Cross multiply
[16b = 9c]
replace c with 4a
16b = 9(4a)
16b = 36a
Divide both sides by 16
b = 36/16xa
Reduce fraction
b = 9/4xa
Substitute in the 1st equation
a + 9/4xa + 4a = 174
multiply by 4 to get rid of denominators:
4a + 9a + 4(4a) = 4(174)
4a + 9a + 16a = 696
29a = 696
a = 696/29
a = 24 is the 1st number
Find the 2nd number
b = 9/4x(24)
b = 9x6
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