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Algebra 1 : Linear Equations

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Example Questions

Example Question #12 : Proportions

I have a bag full of blue and red marbles. If the ratio of blue to red marbles is 1:4 and if I have 16 blue ones, how many red marbles are in the bag.

Possible Answers:

Correct answer:

Explanation:

First, translate the problem into a proportion equation. We have the ratio 1:4. Therefore, we have the fraction $\frac{1}{4}$ . Set that fraction equal to the number of blue (which is 16) marbles divide by the number of red marbles.

$\frac{1}{4}=\frac{16}{r}$

We need to find , the number of red marbles. Perform the cross multiplication

1r=4(16)

r=64

So there are 64 red marbles.

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Example Question #13 : Proportions

If 3x=141 , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

For this problem, we can divide both sides of the original equation by to obtain our answer. Another way we can solve this problem, however, is by using a proportion,

$\frac{3x}{141}=\frac{-x}{y}$

Cross-multiplication yields the equation

3xy=-141x

Dividing both sides by gives us

3y=-141

an equation that can be easily solved to get

y=-47

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Example Question #14 : Proportions

Solve:

$\frac{(x+3)}{4}=\frac{7}{16}$

Possible Answers:

x=5

$x=-\frac{5}{4}$

$x=\frac{1}{}4$

$x=\frac{3}{4}$

x=-3

Correct answer:

$x=-\frac{5}{4}$

Explanation:

Multiply diagonally so that you get 16x+48=28 .

Isolate for and you get $-\frac{20}{16}$ .

Simplify and you get $-\frac{5}{4}$ .

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Example Question #11 : Proportions

$\frac{(9x+5)}{4}=\frac{2x}{8}$

Possible Answers:

$x=-\frac{3}{4}$

$x=-\frac{5}{8}$

x=8

$x=-\frac{8}{5}$

$x=\frac{1}{8}$

Correct answer:

$x=-\frac{5}{8}$

Explanation:

Cross-multiply and you get 8x=72x+40.

Isolate for and you get $-\frac{5}{8}$ .

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Example Question #1141 : Algebra 1

A car uses up gallons of gas in miles. Which expression best represents the distance, in kilometers, that the car can travel on 15 gallons of gas?

(1 mile is equivalent to 1.6 kilometers.)

Possible Answers:

$\frac{75x}{8y}$

$\frac{24y}{x}$

$\frac{75y}{8x}$

90xy

$\frac{24x}{y}$

Correct answer:

$\frac{24y}{x}$

Explanation:

gallons will allow the car to travel miles, or 1.6y kilometers.

Set up a proportion, where is the distance:

$\small \frac{d}{15} = \frac{1.6y}{x}$

Solve for :

$\small d = \frac{1.6y}{x} \cdot 15$

$d = \frac{24y}{x}$

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Example Question #17 : Proportions

Solve: $\frac{x}{2}= \frac{8}{x}$

Possible Answers:

$\pm4$

Correct answer:

$\pm4$

Explanation:

To solve the proportion, cross multiply.

x^2=16

$x=\sqrt{16}$

$x=\pm 4$

The correct answer is $\pm4$ since both numbers satisfy the original problem.

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Example Question #13 : Proportions

Solve for .

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

Possible Answers:

Correct answer:

Explanation:

Cross multiply.

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

We get

$\\1\cdot x=2\cdot 3\\ x=6$ .

That's the answer.

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Example Question #19 : Proportions

Solve for

$\frac{2}{5}=\frac{x}{3}$

Possible Answers:

$\frac{3}{2}$

$\frac{5}{6}$

$\frac{4}{9}$

$\frac{2}{3}$

$\frac{6}{5}$

Correct answer:

$\frac{6}{5}$

Explanation:

Let's cross multiply.

$\frac{2}{5}=\frac{x}{3}$

We have

$\\2\cdot 3=5\cdot x \\6=5x$ .

Divide both sides by .

$x=\frac{6}{5}$ .

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Example Question #20 : Proportions

Solve for .

$\frac{3}{4}=\frac{x}{2}$

Possible Answers:

$\frac{1}{2}$

$\frac{2}{3}$

$\frac{1}{6}$

$\frac{3}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

Let's cross multiply.

$\frac{3}{4}=\frac{x}{2}$

We have

$\\4\cdot x=3\cdot 2\\4x=6$ .

Divide both sides by , we get

$x=\frac{6}{4}=\frac{3}{2}$ .

The answer is reduced and we do that by dividing top and bottom by .

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Example Question #21 : Proportions

Solve for .

$\frac{1}{x}=\frac{7}{9}$

Possible Answers:

$\frac{9}{7}$

$\frac{7}{9}$

$\frac{18}{19}$

Correct answer:

$\frac{9}{7}$

Explanation:

Let's cross multiply.

$\frac{1}{x}=\frac{7}{9}$

We have

$\\7\cdot x=1\cdot 9\\7x=9$ .

Divide both sides by , we get

$x=\frac{9}{7}$ .

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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #12 : Proportions

Example Question #13 : Proportions

Example Question #14 : Proportions

Example Question #11 : Proportions

Example Question #1141 : Algebra 1

Example Question #17 : Proportions

Example Question #13 : Proportions

Example Question #19 : Proportions

Example Question #20 : Proportions

Example Question #21 : Proportions

All Algebra 1 Resources

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