# When the quotient of a certain number and 6 is decreased by 14, the result is 4. Find the number.

## Question:

When the quotient of a certain number and {eq}6 {/eq} is decreased by {eq}14 {/eq}, the result is {eq}4 {/eq}.

Find the number.

## Converting Words to Equations:

In mathematics, it is common to want to convert words to equations in order to use the equations to solve various problems. We can do this by representing certain phrases with mathematical operations and symbols, and creating an equation in the process.

## Answer and Explanation:

In the scenario described, we will start by letting the number in question be *x*. We are given that when the quotient of the number, *x*, and 6 is decreased by 14, the result is 4. The quotient of *x* and 6 can be expressed as the fraction {eq}\frac{x}{6} {/eq}. Thus, we have that {eq}\frac{x}{6} {/eq} minus 14, or {eq}\frac{x}{6}-14 {/eq}, is equal to 4. This gives the following equation.

- {eq}\displaystyle \frac{x}{6}-14=4 {/eq}

We can solve this for *x* to find our number. First, we multiply both sides of the equation by 6 to eliminate fractions.

- {eq}x-84=24 {/eq}

Add 84 to both sides of the equation.

- {eq}x=108 {/eq}

We get that *x* = 108, so the number described is 108.

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from Algebra I: High School

Chapter 8 / Lesson 20