Question

a toy is regularly priced at $111. for a sale, the price was reduced by 65%.
(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: 65, 100, 111, 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:

Part (a)

Step1: Understand Proportion for Percent

A percent reduction means the reduction \( x \) is to the original price (\( 111 \)) as the percent reduction (\( 65 \)) is to \( 100 \) (since percent is out of 100). So the proportion is \(\frac{65}{100}=\frac{x}{111}\).

Step2: Fill the Proportion

Place \( 65 \) over \( 100 \) and \( x \) over \( 111 \) in the proportion boxes. So the proportion is \(\frac{65}{100}=\frac{x}{111}\).

Part (b)

Step1: Solve the Proportion

From \(\frac{65}{100}=\frac{x}{111}\), cross - multiply: \( 100x = 65\times111 \). Then \( x=\frac{65\times111}{100}\). Calculate \( 65\times111 = 7215 \), so \( x=\frac{7215}{100}=72.15 \).

Step2: State the Reduction

The reduction in price \( x \) is \( \frac{65\times111}{100}=72.15 \) dollars.

Part (c)

Step1: Calculate Sale Price

The sale price is the original price minus the reduction. Original price is \( 111 \) dollars, reduction is \( 72.15 \) dollars. So sale price \( = 111 - 72.15 \).

Step2: Compute the Sale Price

\( 111-72.15 = 38.85 \) dollars.

Part (a) Answer: \(\boldsymbol{\frac{65}{100}=\frac{x}{111}}\)

Part (b) Answer: \(\boldsymbol{72.15}\)

Part (c) Answer: \(\boldsymbol{38.85}\)

Answer:

Step1: Calculate Sale Price

The sale price is the original price minus the reduction. Original price is \( 111 \) dollars, reduction is \( 72.15 \) dollars. So sale price \( = 111 - 72.15 \).

Step2: Compute the Sale Price

\( 111-72.15 = 38.85 \) dollars.

Part (a) Answer: \(\boldsymbol{\frac{65}{100}=\frac{x}{111}}\)

Part (b) Answer: \(\boldsymbol{72.15}\)

Part (c) Answer: \(\boldsymbol{38.85}\)