Question

linear equation
writing a proportion to solve a multi - step problem involving percentages
a toy is regularly priced at $117. for a sale, the price was reduced by 45%.
(a) let x be the reduction in price (in dollars). using the values below, create a proportion
that can be used to find x.
values: 45 100 117 x
(b) use the proportion from part (a) to find the reduction in price. do not round any
computations.
reduction in price: $
(c) what was the price of the toy during the sale? do not round any computations.
price during the sale: $
explanation check

Explanation:

Part (a)

Step1: Understand percentage proportion

A percentage reduction means the reduction \( x \) is 45% of the original price (\( \$117 \)). The proportion for percentages is \( \frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100} \), where part is \( x \), whole is \( 117 \), percent is \( 45 \), and 100 is the base of percentage.
So the proportion is \( \frac{x}{117}=\frac{45}{100} \)

Part (b)

Step1: Solve the proportion for \( x \)

From \( \frac{x}{117}=\frac{45}{100} \), cross - multiply: \( 100x = 117\times45 \)

Step2: Calculate \( 117\times45 \)

\( 117\times45=(100 + 17)\times45=100\times45+17\times45 = 4500+765 = 5265 \)

Step3: Solve for \( x \)

\( x=\frac{5265}{100}=52.65 \)

Part (c)

Step1: Subtract reduction from original price

The original price is \( \$117 \), and the reduction is \( \$52.65 \). So the sale price \( = 117 - 52.65 \)

Step2: Calculate the result

\( 117-52.65 = 64.35 \)

Part (a) Answer: \( \boldsymbol{\frac{x}{117}=\frac{45}{100}} \)

Part (b) Answer: \( \boldsymbol{52.65} \)

Part (c) Answer: \( \boldsymbol{64.35} \)

Answer:

Step1: Subtract reduction from original price

The original price is \( \$117 \), and the reduction is \( \$52.65 \). So the sale price \( = 117 - 52.65 \)

Step2: Calculate the result

\( 117-52.65 = 64.35 \)

Part (a) Answer: \( \boldsymbol{\frac{x}{117}=\frac{45}{100}} \)

Part (b) Answer: \( \boldsymbol{52.65} \)

Part (c) Answer: \( \boldsymbol{64.35} \)