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Common Core: 6th Grade Math : Find a Percent of a Quantity as a Rate Per 100: CCSS.Math.Content.6.RP.A.3c

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Example Question #11 : Find A Percent Of A Quantity As A Rate Per 100: Ccss.Math.Content.6.Rp.A.3c

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 800 $\displaystyle 800$ cars in the parking lot and $80\%$ $\displaystyle 80\%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

640 $\displaystyle 640$

630 $\displaystyle 630$

460 $\displaystyle 460$

$\displaystyle 80$

360 $\displaystyle 360$

Correct answer:

640 $\displaystyle 640$

Explanation:

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that $80\%$ $\displaystyle 80\%$ of the cars are red. In other words, for every hundred cars $\displaystyle 80$ of them are red. We can write the following ratio:

$80:100\rightarrow\frac{80}{100}$ $\displaystyle 80:100\rightarrow\frac{80}{100}$

Reduce.

$\frac{80}{100}\rightarrow \frac{8}{10}\rightarrow \frac{4}{5}$ $\displaystyle \frac{80}{100}\rightarrow \frac{8}{10}\rightarrow \frac{4}{5}$

We know that there are 800 $\displaystyle 800$ cars in the parking lot. We can write the following ratio by substituting the variable Red $\displaystyle Red$ for the number of red cars:

$Red:800\rightarrow \frac{Red}{800}$ $\displaystyle Red:800\rightarrow \frac{Red}{800}$

Now, we can create a proportion using our two ratios.

$\frac{4}{5}=\frac{Red}{800}$ $\displaystyle \frac{4}{5}=\frac{Red}{800}$

Cross multiply and solve for Red $\displaystyle Red$ .

$5 \times Red=4\times800$ $\displaystyle 5 \times Red=4\times800$

Simplify.

$\displaystyle 5 Red=3200$

Divide both sides of the equation by $\displaystyle 5$ .

$\frac{5Red}{5}=\frac{3200}{5}$ $\displaystyle \frac{5Red}{5}=\frac{3200}{5}$

Solve.

Red=640 $\displaystyle Red=640$

There are 640 $\displaystyle 640$ red cars in the parking lot.

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Example Question #12 : Find A Percent Of A Quantity As A Rate Per 100: Ccss.Math.Content.6.Rp.A.3c

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 3200 $\displaystyle 3200$ cars in the parking lot and $8\%$ $\displaystyle 8\%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

800 $\displaystyle 800$

256 $\displaystyle 256$

218 $\displaystyle 218$

182 $\displaystyle 182$

188 $\displaystyle 188$

Correct answer:

256 $\displaystyle 256$

Explanation:

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that $8\%$ $\displaystyle 8\%$ of the cars are red. In other words, for every hundred cars $\displaystyle 8$ of them are red. We can write the following ratio:

$8:100\rightarrow\frac{8}{100}$ $\displaystyle 8:100\rightarrow\frac{8}{100}$

Reduce.

$\frac{8}{100}\rightarrow \frac{4}{50}\rightarrow \frac{2}{25}$ $\displaystyle \frac{8}{100}\rightarrow \frac{4}{50}\rightarrow \frac{2}{25}$

We know that there are 3200 $\displaystyle 3200$ cars in the parking lot. We can write the following ratio by substituting the variable Red $\displaystyle Red$ for the number of red cars:

$Red:3200\rightarrow \frac{Red}{3200}$ $\displaystyle Red:3200\rightarrow \frac{Red}{3200}$

Now, we can create a proportion using our two ratios.

$\frac{2}{25}=\frac{Red}{3200}$ $\displaystyle \frac{2}{25}=\frac{Red}{3200}$

Cross multiply and solve for Red $\displaystyle Red$ .

$25 \times Red=2\times3200$ $\displaystyle 25 \times Red=2\times3200$

Simplify.

$\displaystyle 25 Red=6400$

Divide both sides of the equation by $\displaystyle 25$ .

$\frac{25Red}{25}=\frac{6400}{25}$ $\displaystyle \frac{25Red}{25}=\frac{6400}{25}$

Solve.

Red=256 $\displaystyle Red=256$

There are 256 $\displaystyle 256$ red cars in the parking lot.

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Common Core: 6th Grade Math : Find a Percent of a Quantity as a Rate Per 100: CCSS.Math.Content.6.RP.A.3c

Study concepts, example questions & explanations for Common Core: 6th Grade Math

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #11 : Find A Percent Of A Quantity As A Rate Per 100: Ccss.Math.Content.6.Rp.A.3c

Example Question #12 : Find A Percent Of A Quantity As A Rate Per 100: Ccss.Math.Content.6.Rp.A.3c

All Common Core: 6th Grade Math Resources

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