Q14. - Algebra 1

Question

Record your answers on the answer sheet provided by your teacher or on a sheet of paper.

Lucinda is buying a set of patio furniture that is on sale for $\frac{4}{5}$ of the original price. After she uses a $\mathrm{\backslash (}50$ gift certificate, the total cost before sales tax is $\mathrm{\backslash )}222$. What was the original price of the patio furniture?

Step-by-Step Solution

Answer

The original price of the patio furniture is $\$340$.

Step 1. Given information.

Lucinda is buying a set of patio furniture that is on sale for $\frac{4}{5}$ of the original price.

After she uses a $\$50$ gift certificate, the total cost before sales tax is $\$222$.

Step 2. To make an equation of the problem.

Suppose the original price of the furniture is $=\$a$.

The rate of the sale price will be $\frac{4}{5}a$.

The total cost is $\$222$ after she used the $\$50$ gift certificate.

So, the equation of the problem,

$\frac{4}{5}a-50=222$

Step 3. To find the value of x.

To solve the above equation:

$\begin{array}{l}\frac{4}{5}a-50=222\\ \Rightarrow 4a-50\times 5=222\times 5\\ \Rightarrow 4a-250=1110\\ \Rightarrow 4a=1110+250\\ \Rightarrow 4a=1360\\ \Rightarrow a=\frac{1360}{4}\\ \Rightarrow a=\$340\end{array}$

Hence, the original price of the patio furniture is $\$340$.