Question

examine the worked example. then, answer each question.
gordon is a customer service representative for a company that sells silly magnets, signs, and bumper stickers. last week he received 175 orders, 84 of which were for a magnet shaped like a talking foot. what percent of the orders was for the talking foot magnets?
write a proportion to represent the problem. let p represent the percentage of orders that were for the talking foot magnet.
\\(\frac{\square\text{ orders for the talking foot magnets}}{\square\text{ total orders received last week}} = \frac{\square}{100}\\)
\\(100\left(\square\
ight) = \left(\square\
ight)p\\)
\\(\square = p\\)
the talking foot magnets made up \\(\square\\) % of last week’s orders.

Explanation:

Step1: Set up the proportion

The formula for percentage is \(\frac{\text{part}}{\text{whole}}=\frac{\text{percentage}}{100}\). Here, the part is the number of orders for the talking - foot magnets (\(84\)), and the whole is the total number of orders (\(175\)). So the proportion is \(\frac{84}{175}=\frac{p}{100}\).

Step2: Cross - multiply

Cross - multiplying gives \(100\times84 = 175\times p\).

Step3: Solve for \(p\)

First, calculate \(100\times84=8400\). Then, \(p=\frac{8400}{175}\). Since \(8400\div175 = 48\).

Answer:

The proportion is \(\frac{84}{175}=\frac{p}{100}\), after cross - multiplying \(100\times84 = 175\times p\), and \(p = 48\). The talking - foot magnets made up \(48\%\) of last week’s orders. So the blanks are filled as follows: \(\frac{84}{175}=\frac{p}{100}\), \(100\times84=(175)p\), \(48 = p\), and the final percentage is \(48\).