The first of two consecutive integers is 37 less than twice the second. What are the integers?

Question

I have always been good at math but for some reason I have always struggled with word problems. I hope that this site is able to help me.

Answer 1

Let the first integer = x

Let the second integer = x + 1

 

 

Write an equation.

 

x = 2(x + 1) - 37

 

 

Solve for x.

 

x = 2x + 2 - 37

x = 2x - 35

 

 

Subtract 2x on both sides of the equation.

 

-x = -35

 

 

Divide both sides of the equation by -1.

 

x = 35

 

 

Substitute this value of x into the variables.

 

1st integer = 35

2nd integer = 36

 

Answer 2

let the first integer be n and the second be n+1 since they are consecutive

 

according to the given condition n= 2(n+1) -37

                                             n= 2n -35 so n= 35

 

so the numbers are 35 and 36