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In a random sample of $250$ frozen pepperoni pizzas of a particular brand, $7$ do not have enough pepperoni slices. At this rate, how many of $12$ , $000$ frozen pepperoni pizzas of the same brand will not have enough pepperoni slices?

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GCF and LCM: word problems

Full solution

Q. In a random sample of

250

frozen pepperoni pizzas of a particular brand,

7

do not have enough pepperoni slices. At this rate, how many of

12

,

000

frozen pepperoni pizzas of the same brand will not have enough pepperoni slices?

Problem Understanding: Understand the problem. $\newline$ We are given a sample rate of pizzas without enough pepperoni slices and need to apply this rate to a larger quantity of pizzas.
Finding the Rate: Find the rate of pizzas without enough pepperoni slices in the sample. $\newline$ Rate = $\frac{\text{Number of pizzas without enough pepperoni}}{\text{Total number of pizzas in the sample}}$ $\newline$ Rate = $\frac{7}{250}$
Calculating Expected Number: Calculate the expected number of pizzas without enough pepperoni slices in $12,000$ pizzas. $\newline$ Expected number $=$ Rate $\times$ Total number of pizzas $\newline$ Expected number $=$ $\left(\frac{7}{250}\right) \times 12,000$
Performing the Calculation: Perform the calculation. $\newline$ Expected number = $(\frac{7}{250}) \times 12,000$ $\newline$ Expected number = $(7 \times 12,000) / 250$ $\newline$ Expected number = $84,000 / 250$ $\newline$ Expected number = $336$

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