The sum of three numbers is 147. The third number is 4 times the second. The first number is 9 more than the second. What are the number?

First: 32

Second: 23

Third: 92

Step-by-step explanation:

Assign a variable

let "x" be the second number

Then, write equations for the first and third numbers with "x".

x + 9 first number

x second number

4x third number

Write an equation that makes the three numbers equal to 147.

(x + 9) + (x) + (4x) = 147

Remove the brackets

x + 9 + x + 4x = 147

Combine like terms. Add numbers with the variable "x".

x + x + 4x = 6x, so rewrite the equation as:

6x + 9 = 147

Now, isolate "x". Subtract 9 from both sides.

6x = 138

Divide both sides by 6.

x = 23

Now find the first and third number using x = 23 and their equations.

First number: 32

x + 9

= 23 + 9

= 32

Third number: 92

4x

= 4 (23)

= 92

Check your answer by adding all the numbers:

32 + 23 + 92 = 147

Therefore, these numbers are correct.