Question

Two times the least of three consecutive odd integers exceeds three times the greatest by 15. What are the integers?

Short answer

The required integers are $-27,-25$ and $-23$.

Step-by-step solution

Step 1. List the given data.

Two times the least of three consecutive odd integers exceeds three times the greatest by 15.

Step 2. Formulate the equation.

Let the three consecutive odd integers be $x$, $x+2$and $x+4$. Then, the least of them is $x$and the greatest of them is $x+4$.

Translating the given condition into an equation,

$2x-3\left(x+4\right)=15$

Step 3. Solve the obtained equation.

Solving,

$2x-3\left(x+4\right)=15$ (Given equation)

$2x-3x-12=15$ (Distributive property)

$-x-12=15$ (Simplify)

$-x-12+12=15+12$ (Add 12 to both sides)

$-x=27$ (Simplify)

$\frac{-x}{-1}=\frac{27}{-1}$ (Divide both sides by $-1$)

$x=-27$ (Simplify)

So, $x=-27$is the solution of the given equation.

Step 4. Interpret the obtained solution.

The required integers were assumed to be $x$, $x+2$and $x+4$. It was obtained that for the given condition to be satisfied, $x=-27$.

Then, the required integers are $\mathbf{-}\mathbf{27}\mathbf{,}\mathbf{}\mathbf{-}\mathbf{25}$and $\mathbf{-}\mathbf{23}$.