Ratios & Proportional Relationships - 6th Grade Math

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Question

Candidate A receives votes for every vote that candidate B receives. At the end of the election candidate B has votes. How many votes did candidate A get?

Answer

In order to solve this problem we need to create a ratio with the given information. It says that for every votes cast for candidate A, candidate B got vote. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$3:1\rightarrow \frac{3}{1}$

We know that candidate B received votes. Write a new ratio.

$A:900\rightarrow\frac{A}{900}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{3}{1}=\frac{A}{900}$

Cross multiply and solve for .

Simplify and solve.

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Question

At a car production company, manufacturers place tires and transmission on every car in the production line. A manager orders tires, how many transmissions should he order?

Answer

In order to solve this problem we must make a table of ratios. In the question we are given the base ratio:

$4\ \text{tires}:1\ \text{transmission}$

We can use this ratio to make a table.

According to the table, the manager should order $2\ \text{transmissions}$ .

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Question

At a car production company, manufacturers place tires and transmission on every car in the production line. A manager orders tires, how many transmissions should he order?

Answer

In order to solve this problem we must make a table of ratios. In the question we are given the base ratio:

$4\ \text{tires}:1\ \text{transmission}$

We can use this ratio to make a table.

According to the table, the manager should order $5\ \text{transmissions}$ .

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Question

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

Answer

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 of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$60:100\rightarrow\frac{60}{100}$

Reduce.

$\frac{60}{100}\rightarrow \frac{6}{10}\rightarrow \frac{3}{5}$

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

$Red:100\rightarrow \frac{Red}{100}$

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

$\frac{3}{5}=\frac{Red}{100}$

Cross multiply and solve for .

$5 \times Red=3\times100$

Simplify.

Divide both sides of the equation by .

$\frac{5Red}{5}=\frac{300}{5}$

Solve.

There are red cars in the parking lot.

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Question

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

Answer

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 of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$10:100\rightarrow\frac{10}{100}$

Reduce.

$\frac{10}{100}\rightarrow \frac{1}{10}$

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

$Red:250\rightarrow \frac{Red}{250}$

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

$\frac{1}{10}=\frac{Red}{250}$

Cross multiply and solve for .

$10 \times Red=1\times 250$

Simplify.

Divide both sides of the equation by .

$\frac{10Red}{10}=\frac{250}{10}$

Solve.

There are red cars in the parking lot.

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Question

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

Answer

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 of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$25:100\rightarrow\frac{25}{100}$

Reduce.

$\frac{25}{100}\rightarrow \frac{1}{4}$

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

$Red:136\rightarrow \frac{Red}{136}$

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

$\frac{1}{4}=\frac{Red}{136}$

Cross multiply and solve for .

$4 \times Red=1\times136$

Simplify.

Divide both sides of the equation by .

$\frac{4Red}{4}=\frac{136}{4}$

Solve.

There are red cars in the parking lot.

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Question

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

Answer

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 of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$25:100\rightarrow\frac{25}{100}$

Reduce.

$\frac{25}{100}\rightarrow \frac{1}{4}$

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

$Red:164\rightarrow \frac{Red}{164}$

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

$\frac{1}{4}=\frac{Red}{164}$

Cross multiply and solve for .

$4 \times Red=1\times164$

Simplify.

Divide both sides of the equation by .

$\frac{4Red}{4}=\frac{164}{4}$

Solve.

There are red cars in the parking lot.

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Question

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

Answer

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 of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$60:100\rightarrow\frac{60}{100}$

Reduce.

$\frac{60}{100}\rightarrow \frac{6}{10}\rightarrow \frac{3}{5}$

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

$Red:135\rightarrow \frac{Red}{135}$

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

$\frac{3}{5}=\frac{Red}{135}$

Cross multiply and solve for .

$5 \times Red=3\times135$

Simplify.

Divide both sides of the equation by .

$\frac{5Red}{5}=\frac{405}{5}$

Solve.

There are red cars in the parking lot.

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Question

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

Answer

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 of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$40:100\rightarrow\frac{40}{100}$

Reduce.

$\frac{40}{100}\rightarrow \frac{4}{10}\rightarrow \frac{2}{5}$

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

$Red:400\rightarrow \frac{Red}{400}$

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

$\frac{2}{5}=\frac{Red}{400}$

Cross multiply and solve for .

$5 \times Red=2\times400$

Simplify.

Divide both sides of the equation by .

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

Solve.

There are red cars in the parking lot.

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Question

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

Answer

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 of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$50:100\rightarrow\frac{50}{100}$

Reduce.

$\frac{50}{100}\rightarrow \frac{5}{10}\rightarrow \frac{1}{2}$

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

$Red:200\rightarrow \frac{Red}{200}$

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

$\frac{1}{2}=\frac{Red}{200}$

Cross multiply and solve for .

$2 \times Red=1\times200$

Simplify.

Divide both sides of the equation by .

$\frac{2Red}{2}=\frac{200}{2}$

Solve.

There are red cars in the parking lot.

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Question

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

Answer

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 of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$30:100\rightarrow\frac{30}{100}$

Reduce.

$\frac{30}{100}\rightarrow \frac{3}{10}$

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

$Red:300\rightarrow \frac{Red}{300}$

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

$\frac{3}{10}=\frac{Red}{300}$

Cross multiply and solve for .

$10 \times Red=3\times300$

Simplify.

Divide both sides of the equation by .

$\frac{10Red}{10}=\frac{900}{10}$

Solve.

There are red cars in the parking lot.

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Question

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

Answer

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 of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$4:100\rightarrow\frac{4}{100}$

Reduce.

$\frac{4}{100}\rightarrow \frac{2}{50}\rightarrow \frac{1}{25}$

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

$Red:40\rightarrow \frac{Red}{400}$

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

$\frac{1}{25}=\frac{Red}{400}$

Cross multiply and solve for .

$25 \times Red=1\times400$

Simplify.

Divide both sides of the equation by .

$\frac{25Red}{25}=\frac{400}{25}$

Solve.

There are red cars in the parking lot.

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Question

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

Answer

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 of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$35:100\rightarrow\frac{35}{100}$

Reduce.

$\frac{35}{100}\rightarrow \frac{7}{20}$

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

$Red:200\rightarrow \frac{Red}{200}$

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

$\frac{7}{20}=\frac{Red}{200}$

Cross multiply and solve for .

$20 \times Red=7\times200$

Simplify.

Divide both sides of the equation by .

$\frac{20Red}{20}=\frac{1400}{20}$

Solve.

There are red cars in the parking lot.

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Question

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

Answer

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 of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

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

Reduce.

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

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

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

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

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

Cross multiply and solve for .

$5 \times Red=4\times800$

Simplify.

Divide both sides of the equation by .

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

Solve.

There are red cars in the parking lot.

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Question

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

Answer

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 of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

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

Reduce.

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

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

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

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

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

Cross multiply and solve for .

$25 \times Red=2\times3200$

Simplify.

Divide both sides of the equation by .

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

Solve.

There are red cars in the parking lot.

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Question

At a local microchip factory, there are managers for every workers. How many managers are needed for workers?

Answer

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $25\ \text{workers}$ .

The factory will need $10\ \text{managers}$ .

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Question

At a local microchip factory, there are managers for every workers. How many managers are needed for workers?

Answer

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $5\ \text{workers}$ .

The factory will need $2\ \text{managers}$ .

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Question

At a local microchip factory, there are managers for every workers. How many managers are needed for workers?

Answer

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $15\ \text{workers}$ .

The factory will need $6\ \text{managers}$ .

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Question

At a local microchip factory, there are managers for every workers. How many managers are needed for workers?

Answer

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $10\ \text{workers}$ .

The factory will need $4\ \text{managers}$ .

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Question

At a local microchip factory, there are managers for every workers. How many managers are needed for workers?

Answer

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $60\ \text{workers}$ .

The factory will need $24\ \text{managers}$ .

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