Q28. - Algebra 1

Question

Write an equation and solve each problem.

Find four consecutive integers with the sum of 54.

Step-by-Step Solution

Answer

The required consecutive integers are 12, 13, 14 and 15.

Step 1. List the given data.

The sum of four consecutive integers is 54.

Step 2. Write the equation for the given problem.

Let $x$ be the first integer. Then, the four consecutive integers are $x$, $x+1$, $x+2$ and $x+3$.

 

Translating the given problem into equation form,

 

$x+x+1+x+2+x+3=54$

 

This is the required equation for the given problem.

Step 3. Solve the equation.

Solving,

 

$x+x+1+x+2+x+3=54$  (Obtained equation)

 

$4x+6=54$  (Simplify)

 

$4x+6-6=54-6$  (Subtract 6 from both sides)

 

$4x=48$  (Simplify)

 

$\frac{4x}{4}=\frac{48}{4}$  (Divide both sides by 4)

 

$x=12$  (Simplify)

 

So, $x=12$ is the solution of the obtained equation.

Step 4. Interpret the obtained solution.

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

 

Thus, the required consecutive integers are 12, 13, 14 and 15.