Q27. - Algebra 1

Question

Write an equation and solve each problem.

Find three consecutive odd integers with the sum of 141.

Step-by-Step Solution

Answer

The required consecutive odd integers are 45, 47 and 49.

Step 1. List the given data.

The sum of three consecutive odd integers is 141.

Step 2. Write the equation for the given problem.

Let $x$ be the first odd integer. Then, the three consecutive odd integers are $x$, $x+2$ and $x+4$.

 

Translating the given problem into equation form,

 

$x+x+2+x+4=141$

 

This is the required equation for the given problem.

Step 3. Solve the equation.

Solving,

 

$x+x+2+x+4=141$  (Obtained equation)

 

$3x+6=141$  (Simplify)

 

$3x+6-6=141-6$  (Subtract 6 from both sides)

 

$3x=135$  (Simplify)

 

$\frac{3x}{3}=\frac{135}{3}$  (Divide both sides by 3)

 

$x=45$  (Simplify)

 

So, $x=45$ is the solution of the obtained equation.

Step 4. Interpret the obtained solution,

According to the assumption, $x$ is the first of the three required consecutive odd integers which satisfy the given problem.

 

Thus, the required consecutive odd integers are 45, 47 and 49.