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Algebra 1 : Proportions

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Example Questions

Example Question #1 : Proportions

The probability of an event is 3/11. Find the chance the event will not occur.

Possible Answers:

3/11

8/3

11/3

8/11

3/8

Correct answer:

8/11

Explanation:

If the chance an event will happen is 3/11, that means there are 8 instances where the even would not occur out of every 11, giving us 8/11.

3 chances out of 11 = event

11 – 3 = 8

8 chances out of 11 = no event

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Example Question #2 : Proportions

Solve for :

$\small \frac{4}{7} = \frac{x}{28}$

Possible Answers:

Correct answer:

Explanation:

Cross multiply:

$\small 7x\ =\ 4\times 28\ =112$

Solve for :

$\small 7x\ =\ 112$

$\frac{112}{7}=16$

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Example Question #3 : Proportions

Solve for in the following proportion statement:

$\small \frac{n}{4\frac{1}{2}} = \frac{4\frac{2}{3}}{2\frac{1}{4}}$

Possible Answers:

$\small 9\tfrac{1}{2}$

$\small 9\tfrac{1}{3}$

$\small 8\tfrac{1}{2}$

$\small 8\tfrac{1}{12}$

$\small 8\tfrac{2}{3}$

Correct answer:

$\small 9\tfrac{1}{3}$

Explanation:

Use cross-multiplication to set up the following equation:

$\small \frac{n}{4\frac{1}{2}} = \frac{4\frac{2}{3}}{2\frac{1}{4}}$

$\small 2\tfrac{1}{4} \cdot n = 4\tfrac{1}{2} \cdot 4\tfrac{2}{3}$

Rewrite with improper fractions and solve:

$\small \small \frac{9}{4} \cdot n = \frac{9}{2} \cdot \frac{14}{3} = \frac{3}{1} \cdot \frac{7}{1} = \frac{21}{1}$

$\small n= \frac{21}{1} \div \frac{9}{4} = \frac{21}{1} \cdot \frac{4}{9} = \frac{7}{1} \cdot \frac{4}{3} = \frac{28}{3} = 9 \frac{1}{3}$

So the correct choice is $\small 9 \frac{1}{3}$ .

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Example Question #3 : Proportions

$\textup{A taste test shows that out of every 5 people who participated, 3 of them preferred}$

$\textup{OK Cola to ABC Root Beer. If 100 people participated, how many preferred OK Cola?}$

Possible Answers:

Correct answer:

Explanation:

$\textup{Set up an equation with the two proportions: }\frac{3}{5}=\frac{x}{100}$

$\textup{Cross multiply and solve: }5x=300\;\;\;\;\;\;\;\;\;x=60$

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Example Question #2 : Proportions

If Max drives 10 miles in 24 minutes, how many minutes will it take for him to drive 25 miles?

Possible Answers:

$48\ minutes$

$60\ hours$

$36\ minutes$

$75\ minutes$

$60\ minutes$

Correct answer:

$60\ minutes$

Explanation:

Set up a proportion, with miles driven on top and the time (in minutes) on the bottom:

$\frac{10}{24} = \frac{25}{x}$

Then, cross multiply:

10x = 24(25) , or

10x = 600

Finally, dividing both sides by 10 gives:

x = 60 minutes.

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Example Question #2 : Proportions

A recipe for making 24 cookies calls for 6 cups of sugar. How many cups of sugar would be needed to make 16 cookies?

Possible Answers:

Correct answer:

Explanation:

To solve the equation, you can set up a proportion with as the cups of sugar needed for making cookies. In this case, we know that it takes 6 cups of sugar to make 24 cookies, so we can set up the proportion as $\frac{x}{y}=\frac{6}{24}$ . Since we know that we need to make 16 cookies, we can substitute 16 for , $\frac{x}{16}=\frac{6}{24}$ . Cross multiply the fractions to get 24x=96 . Now, solve for to get a solution of 4.

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Example Question #3 : Proportions

$\textup{A bag contains 60 marbles, all of which are either red, white, or blue.}$

$\textup{If }\frac{2}{5}\textup{ of the marbles are red and }\frac{1}{4}\textup{ of the marbles are white,}$

$\textup{how many blue marbles are in the bag?}$

Possible Answers:

Correct answer:

Explanation:

$\textup{Probability}= \frac{\textup{desired outcomes}}{\textup{total outcomes}}$

$\textup{ First find out how many red and white marbles there are.}$

$\textup{Red: }\frac{2}{5}=\frac{r}{60}\;\;\;5r=120\;\;\;r=24\;\;\;$

$\textup{White: }\frac{1}{4}=\frac{w}{60}\;\;\;4w=60\;\;\;w=15$

$\textup{Blue: }b = 60-24-15\;\;\;\;\;b=21$

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Example Question #4 : Proportions

To make 36 cookies, a recipe calls for 5 ounces of chocolate chips. How many ounces of chocolate chips would you need to make 900 cookies?

Possible Answers:

130

115

120

125

None of the other answers

Correct answer:

125

Explanation:

To figure out how many ounces of chocolate chips are needed to make 900 cookies, you simply need to set up a proportion. In this case, we know that 5 ounces of chocolate chips are needed to make 36 cookies, and we are trying to make a total of 900 cookies. Therefore, you can set up the proportion as

$\frac{5}{36}=\frac{x}{900}$

where is the ounces of chocolate chips needed to make 900 cookies.

For this proportion, solving for would give you a result of 125 ounces of chocolate chips.

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Example Question #3 : Proportions

If $\frac{3}{x} = \frac{x+4}{20}$ , what is the value of ?

Possible Answers:

x=8

x=5

x=10 , x=-6

x=-3 , x=-24

x=6 , x=-10

Correct answer:

x=6 , x=-10

Explanation:

Proportions are useful for solving many types of problems, but here our equation itself is a proportion.

To solve, we cross-multiply: the numerator of one side times the denominator of the other and vice versa. We are left with

$x^{2}+4x=60$ or

$x^{2}+4x-60=0$

A simple FOIL gives us (x-6)(x+10)=0

so our solutions are x=6 and x=-10 .

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Example Question #5 : Proportions

If 9x = 17y , what is the value of 24x ?

Possible Answers:

49.5y

9.1y

12.7y

36.2y

45.3y

Correct answer:

45.3y

Explanation:

To solve this equation, we need to set up a simple proportion. Since the variables and are already in use, let's call the quantity that we are solving for . From the given information, we know we can use the proportion $\frac{9x}{17y} = \frac{24x}{z}$ . Cross-multiplication yields (9x)(z) = (24x)(17y) . Dividing by the common term of and simplifying the right side gives us 9z = 408y , so our solution must be 45.3y .

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Algebra 1 : Proportions

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : Proportions

Example Question #2 : Proportions

Example Question #3 : Proportions

Example Question #3 : Proportions

Example Question #2 : Proportions

Example Question #2 : Proportions

Example Question #3 : Proportions

Example Question #4 : Proportions

Example Question #3 : Proportions

Example Question #5 : Proportions

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