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Algebra 1 : Linear Equations

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Example Questions

Example Question #1 : 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 #1 : Proportions

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

Possible Answers:

$75\ minutes$

$36\ minutes$

$48\ minutes$

$60\ hours$

$60\ minutes$

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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Example Question #11 : Proportions

Find .

$\frac{2}{9}=\frac{x}{36}$

Possible Answers:

Correct answer:

Explanation:

This is a proportion problem. To find , we can use the cross-multiply method. This methods works by, first, multiplying the numerator of the first fraction with the denominator of the second fraction. Set this multiplication equal to the multiplication of the denominator of the first fraction with the numerator of the second fraction. In our problem, this is written as

2(36)=9x

72=9x

divide by 9

$\frac{72}{9}=\frac{9x}{9}$

x=8

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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : Proportions

Example Question #3 : Proportions

Example Question #3 : Proportions

Example Question #1 : Proportions

Example Question #2 : Proportions

Example Question #3 : Proportions

Example Question #4 : Proportions

Example Question #3 : Proportions

Example Question #5 : Proportions

Example Question #11 : Proportions

All Algebra 1 Resources

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