Q5. - Algebra 2

Question

If the product of $\left(2+3\right),\left(3+4\right)\text{ and }\left(4+5\right)$ is equal to three times the sum of 40 and x, then $x=$.

Step-by-Step Solution

Answer

The values of x is 65.

Step-1 – Apply the concept of Verbal and Algebraic expression and Variable

The algebraic expression is obtained from verbal expression using mathematical operators like addition $+$, subtraction $-$, multiplication $\times$, division $÷$ and many such more and variable.

In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol. 

Step-2 – Example for the variable

In the expression  $4x+1$, the unknown quantity is x. So, the variable in this expression is x. 4 and 1 are constants values.

Step-3 – Construct the Algebraic expression

Consider the provided verbal expression.

The product of $\left(2+3\right),\left(3+4\right),\left(4+5\right)$ is equal to three times the sum of 40 and x.

The mathematical operators corresponding to product is multiplication $\times$ and to times is multiplication $\times$.

Express the verbal expression as provided below.

$\begin{array}{c}\left(2+3\right)\times \left(3+4\right)\times \left(4+5\right)=3\left(40+x\right)\\ 5\times 7\times 9=3\left(40+x\right)\\ 315=120+3x\end{array}$

Simplify the expression for the value of x.

$\begin{array}{c}315-120=3x\\ 195=3x\\ x=\frac{195}{3}\\ x=65\end{array}$

Hence, the value of x is 65.