6th Grade Math - Understand the Concept of a Ratio: CCSS.Math.Content.6.RP.A.1

If 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?

Explanation

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.

$5:1\rightarrow \frac{5}{1}$

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

$A:37\rightarrow\frac{A}{37}$

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

$\frac{5}{1}=\frac{A}{37}$

Cross multiply and solve for .

Simplify and solve.

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?

Explanation

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.

$7:1\rightarrow \frac{7}{1}$

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

$A:134\rightarrow\frac{A}{134}$

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

$\frac{7}{1}=\frac{A}{134}$

Cross multiply and solve for .

Simplify and solve.

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

$533\tfrac{1}{3}$

$325\tfrac{2}{3}$

Explanation

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 votes. We can write the following ratio.

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

Now substitute in the given numbers.

$5:3\rightarrow \frac{5}{3}$

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

$A:320\rightarrow\frac{A}{320}$

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

$\frac{5}{3}=\frac{A}{320}$

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

$\frac{3A}{3}=\frac{1600}{3}$

Solve.

$A=533\tfrac{1}{3}$

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

Explanation

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

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

Now substitute in the given numbers.

$1:5\rightarrow \frac{1}{5}$

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

$A:320\rightarrow\frac{A}{320}$

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

$\frac{1}{5}=\frac{A}{320}$

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

$\frac{5A}{5}=\frac{320}{5}$

Solve.

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

Explanation

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

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

Now substitute in the given numbers.

$1:2\rightarrow \frac{1}{2}$

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

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

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

$\frac{1}{2}=\frac{A}{300}$

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

$\frac{2A}{2}=\frac{300}{2}$

Solve.

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?

Explanation

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.

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

$127\tfrac{1}{2}$

Explanation

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 votes. We can write the following ratio.

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

Now substitute in the given numbers.

$3:6\rightarrow \frac{3}{6}$

Reduce.

$\frac{3}{6}=\frac{1}{2}$

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

$A:320\rightarrow\frac{A}{255}$

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

$\frac{1}{2}=\frac{A}{255}$

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

$\frac{2A}{2}=\frac{255}{2}$

Solve.

$A=127\tfrac{1}{2}$

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

$66\tfrac{1}{2}$

Explanation

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 votes. We can write the following ratio.

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

Now substitute in the given numbers.

$7:4\rightarrow \frac{7}{4}$

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

$A:38\rightarrow\frac{A}{38}$

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

$\frac{7}{4}=\frac{A}{38}$

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

$\frac{4A}{4}=\frac{266}{4}$

Solve.

$A=66\tfrac{1}{2}$

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

$106\tfrac{2}{3}$

Explanation

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

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

Now substitute in the given numbers.

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

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

$A:320\rightarrow\frac{A}{320}$

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

$\frac{1}{3}=\frac{A}{320}$

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

$\frac{3A}{3}=\frac{320}{3}$

Solve.

$A=106\tfrac{2}{3}$

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

$162\tfrac{5}{9}$

Explanation

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 votes. We can write the following ratio.