About Solving Proportion Equations:
When we encounter a proportion equation, our first step is to clean up the equation by cross multiplying. We can then solve our proportion equation using the four-step method for solving equations.
Test Objectives
- Demonstrate the ability to solve a proportion equation
- Demonstrate the ability to solve a proportion word problem
#1:
Instructions: solve each equation.
$$a)\hspace{.2em}\frac{12}{6}=\frac{x}{3}$$
$$b)\hspace{.2em}\frac{12}{8x}=\frac{3}{10}$$
$$c)\hspace{.2em}\frac{x - 2}{5}=\frac{x + 11}{4}$$
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#2:
Instructions: solve each equation.
$$a)\hspace{.2em}\frac{7}{12}=\frac{x + 9}{x - 2}$$
$$b)\hspace{.2em}\frac{5}{x + 5}=-\frac{7}{x - 4}$$
$$c)\hspace{.2em}\frac{6}{x - 10}=\frac{2}{x + 3}$$
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#3:
Instructions: solve each equation.
$$a)\hspace{.2em}\frac{x + 1}{12}=\frac{x - 5}{2}$$
$$b)\hspace{.2em}\frac{7}{x + 9}=-\frac{6}{x - 4}$$
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#4:
Instructions: solve each equation.
$$a)\hspace{.2em}\frac{x - 2}{x - 6}=\frac{9}{6}$$
$$b)\hspace{.2em}\frac{x - 8}{x - 5}=-\frac{4}{12}$$
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#5:
Instructions: solve each equation.
a) James purchases 6 gallons of premium gasoline for a total price of $19.56. A few moments later, Jennifer fills up her 15 gallon tank with the same premium gasoline. What was the price per gallon of gas? How much was Jennifer’s bill?
b) When using Maxine’s super degreaser for pots and pans, ¼ of a cup of the degreaser should be mixed with 1 gallon of hot water. How much of Maxine’s super degreaser should be mixed with 10 ½ gallons of hot water?
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}x=6$$
$$b)\hspace{.2em}x=5$$
$$c)\hspace{.2em}x=-63$$
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#2:
Solutions:
$$a)\hspace{.2em}x=-\frac{122}{5}$$
$$b)\hspace{.2em}x=-\frac{5}{4}$$
$$c)\hspace{.2em}x=-\frac{19}{2}$$
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#3:
Solutions:
$$a)\hspace{.2em}x=\frac{31}{5}$$
$$b)\hspace{.2em}x=-2$$
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#4:
Solutions:
$$a)\hspace{.2em}x=14$$
$$b)\hspace{.2em}x=\frac{29}{4}$$
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#5:
Solutions:
a) $3.26 per gallon, Jennifer’s Bill: $48.90
b) 2 5/8 cups
