Question

Write an equation and solve each problem. Find three consecutive odd integers with a sum of 75.

Short answer

The equation of a given situation is $x+(x+2)+(x+4)=75$.

The three consecutive integers whose sum is 75 are 23, 25 and 27.

Step-by-step solution

Step 1. Make the equation.

The sum of three consecutive odd integers is 75.

Assume that the smallest integer be x.

So, the equation is $x+(x+2)+(x+4)=75$.

Step 2. Find the value of x from the equation.

$\begin{array}{l}x+(x+2)+(x+4)=75\\ x+x+2+x+4=75\\ 3x+6=75\\ 3x=75-6\\ 3x=69\\ x=\frac{69}{3}\\ x=23\end{array}$

Step 3. Write three consecutive integers whose sum is 75.

The three consecutive odd integers are 23, $23+2=25$and $23+4=27$.