# The difference between 5 times a number and 20 equals the sum of the number and 40. Find the number.

## Question:

The difference between {eq}5 {/eq} times a number and {eq}20 {/eq} equals the sum of the number and {eq}40 {/eq}.

Find the number.

## Linear Equations:

An equation of the form ax+b =c is called a linear equation, where a, b and c are constants and x is a variable.

Here, we will use the concept of converting words into linear expressions and then using the condition given to establish a linear equation. After that, we will find the value of the unknown asked.

## Answer and Explanation:

{eq}\text{Let}\; x \;\text{be that number}\\ \text{As given, the difference between 5 times the number and 20 equals the sum of the number and 40}\\ \text{At first, we express the difference between 5 times the number and 20},\\ \text{5 times the number will be}\;5x,\\ \text{so, the difference between 5 times the number and 20}\;=\;5x-20,\\ \text{Now, the sum of the number and 40}\;=\;x+40,\\ \text{As per question}\;5x-20\;=\;x+40,\\ or:\;5x-x=40+20\\ or:\;x=15\\ \text{Hence, our answer is}\; 15\\ {/eq}

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