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6th Grade Math : Number Sense

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Example Question #1 : 6th Grade Math

If candidate A receives $\displaystyle 1$ vote for every $\displaystyle 3$ votes that candidate B receives. At the end of the election candidate B has 320 $\displaystyle 320$ votes. How many votes did candidate A get?

Possible Answers:

320 $\displaystyle 320$

$\displaystyle 3$

$\displaystyle 1$

$106\tfrac{2}{3}$ $\displaystyle 106\tfrac{2}{3}$

Correct answer:

$106\tfrac{2}{3}$ $\displaystyle 106\tfrac{2}{3}$

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every $\displaystyle 1$ vote cast for candidate A, candidate B got $\displaystyle 3$ votes. We can write the following ratio.

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

Now substitute in the given numbers.

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

We know that candidate B received 320 $\displaystyle 320$ votes. Write a new ratio.

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

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

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

Cross multiply and solve for $\displaystyle A$.

$\displaystyle 3(A)=320(1)$

Simplify.

3A=320 $\displaystyle 3A=320$

Divide both sides of the equation by $\displaystyle 3$.

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

Solve.

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

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6th Grade Math : Number Sense

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

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Example Question #1 : 6th Grade Math

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