Question

Write an equation and solve each problem.

The ages of three brothers are consecutive integers with the sum of 96. How old are the brothers?

Short answer

The brothers are respectively 31, 32 and 33 years old.

Step-by-step solution

Step 1. List the given data.

The ages of three brothers are consecutive integers with the sum of 96.

Step 2. Write the equation for the given problem.

Let $x$be the first integer representing the age of a brother.

Then, the three consecutive integers representing the ages of the brothers are $x$, $x+1$and $x+2$.

Translating the given problem into equation form,

$x+x+1+x+2=96$

This is the required equation for the given problem.

Step 3. Solve the equation.

Solving,

$x+x+1+x+2=96$ (Obtained equation)

$3x+3=96$ (Simplify)

$3x+3-3=96-3$ (Subtract 3 from both sides)

$3x=93$ (Simplify)

$\frac{3x}{3}=\frac{93}{3}$ (Divide both sides by 3)

$x=31$ (Simplify)

So, $x=31$is the solution of the obtained equation.

Step 4. Interpret the obtained solution.

According to the assumption, $x$is the first of the three consecutive integers which represents the ages of the brothers in the given problem.

Thus, the ages of the three brothers, in order are 31, 32 and 33.