Question

Translate the following verbal statement into an algebraic equation and then solve: Alex brought a refrigerator on sale for 400$ which was two-fifths of the original price. What was the original price of the refrigerator

Answer 1

Let x be the original price of the refrigerator.

Since Alex bought the refrigerator for 2/5 of the original price, we can express that amount algebraically as:

`(2)/(5)x`

On the other hand, he paid $400. Then, we can write down the equation:

`(2)/(5)x=400`

To solve the equation, multiply both members by 5 to get rid of the denominator on the left member:

`\begin{gathered} \Rightarrow5*(2)/(5)x=5*400 \\ \Rightarrow2x=2000 \end{gathered}`

Next, divide both members by 2 to get rid of the factor of 2 that multiplies x:

`\begin{gathered} \Rightarrow(2x)/(2)=(2000)/(2) \\ \Rightarrow x=1000 \end{gathered}`

Therefore, the original price of the refrigerator was $1000.