Question

The sum of three numbers is 174. the ratio of the second number to the third number is 9:16, and the ratio of the first to the third number is 1:4. what is the second number

Answer 1

Let the third number be 16a

Second number = 9a

First number = 4a

According to question,

16a + 9a + 4a = 174

=> 29a = 174

=> a = 174 / 29

=> a = 6

First number = 16 × 6 = 96

Second number = 9 × 6 = 54

Third number = 4 × 6 = 24

Answer 2

Answer:

54

Step-by-step explanation:

54

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