### About Solving Proportions:

A proportion states that two ratios/rates are equal. We can check to see if we have a proportion by cross multiplying. When the cross products are equal, we know we have a proportion. We solve a proportion equation by cross multiplying and using our four-step method for solving equations.

Test Objectives

- Demonstrate the ability to determine if two ratios/rates represent a proportion
- Demonstrate the ability to solve a proportion equation
- Demonstrate the ability to solve a proportion word problem

#1:

Instructions: Solve each equation.

$$a)\hspace{.1em}\frac{12}{10}=\frac{x}{x - 3}$$

$$b)\hspace{.1em}\frac{-7p}{p + 4}=\frac{-3}{10}$$

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#2:

Instructions: Solve each equation.

$$a)\hspace{.1em}\frac{k + 8}{12}=\frac{5k + 6}{4}$$

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#3:

Instructions: Solve each equation.

$$a)\hspace{.1em}\frac{4}{r - 3}=\frac{12}{11r - 1}$$

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#4:

Instructions: Solve each equation.

$$a)\hspace{.1em}\frac{y - 10}{2y + 8}=\frac{-11}{12}$$

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#5:

Instructions: Solve each equation.

a) If 7 gallons of gas cost $27.58, how much would it cost to fill a 40-gallon tank?

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Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}x=18$$

$$b)\hspace{.1em}p=\frac{12}{67}$$

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#2:

Solutions:

$$a)\hspace{.1em}k=\frac{-5}{7}$$

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#3:

Solutions:

$$a)\hspace{.1em}r=-1$$

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#4:

Solutions:

$$a)\hspace{.1em}y=\frac{16}{17}$$

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#5:

Solutions:

a) It would cost $157.60 to fill a 40-gallon tank.