Q9. - Algebra 1

Question

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

Step-by-Step Solution

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 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 $23+4=27$.