Q35. - Algebra 1

Question

CONSECUTIVE INTEGERS find three consecutive odd integers with a sum of 63.

Step-by-Step Solution

Answer

The three numbers are $19,21,23$.

Step 1. Assign variables for the numbers.

A variable is a letter or a literal used to signify an unknown quantity.

Let letter $x$ represent the first number then next two odd consecutive numbers will be $x+2$ and $x+4$.

Step 2. Form an equation for the sum of numbers.

It is given that the sum of numbers is $63$ thus, we have:

$x+\left(x+2\right)+\left(x+4\right)=63$

Step 3. Simplify the equation.

We obtained the equation $x+\left(x+2\right)+\left(x+4\right)=63$, to simplify it, we open the brackets as shown:

$\begin{array}{l}x+\left(x+2\right)+\left(x+4\right)=63\\ x+x+2+x+4=63\end{array}$

Like terms are the terms having same variables and is raised to the same index. Coefficient is the appended number in front of the variable; if no number is shown then we assume it to be 1.

Unlike terms are the terms not having same variables and or are raised to the different index.

For example 4 and $5x$ are unlike terms.

We can add like terms by adding their coefficients, we cannot add unlike terms.

Now we are having the expression $x+x+2+x+4=63$, combining like terms we get:

$\begin{array}{l}x+x+2+x+4=63\\ 3x+6=63\end{array}$

Step 4. Solve the equation.

Now we are having the expression $3x+6=63$, adding $-6$ both sides we get:

$\begin{array}{l}3x+6-6=63-6\\ 3x=57\end{array}$

Dividing both sides by 3 we get:

$\begin{array}{l}\frac{3x}{3}=\frac{57}{3}\\ x=19\end{array}$

Thus the first number is $19$.

Step 5. Use value of first number to get the other numbers.

We know that first number is , thus the other consecutive numbers must be $21$ and $23$.