Question

A store has a 25\%25% off sale on coats. With this discount, the price of one coat is \$34.50$34.50. What is the original price of the coat?

Answer 1

Answer:

$46

Step-by-step explanation:

A percent is a portion of 100. If  we receive 25% off then we pay 75% of the price. 100%-25%=75%. $34.50 is 75% of the original price. We find the new price through a proportion. A proportion is an equation where two ratios or fractions are equal. The ratios or fractions compare like quantities. For example, we will compare percent over percent to an equal ratio of $ to $.

$\frac{75}{100} =\frac{34.50}{y}$

I can now cross-multiply by multiplying numerator and denominator from each ratio.

$75y=100(34.50)\\75y=3450$

I now solve for y by dividing by 75.

$\frac{75y}{75} =\frac{3450}{75} \\y= 46....$

The original price was $46.