COURSE 3 LESSON 5-3
Write an Equation
An old formula for making polish calls for 1 part of
boiled linseed oil for every 3 parts of turpentine. How much
linseed oil is needed to make 10 cups of the polish?
The total amount of polish is 10 cups. The ratio of linseed oil to turpentine is
1 : 3. Find the amount of linseed oil needed for 10 cups of polish.
To find out how much linseed oil you need, set up an equation.
First, use the variable a in a ratio that represents the unknown amounts of
linseed oil and turpentine.
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COURSE 3 LESSON 5-3
Write an Equation
(continued)
ratio
linseed oil
1
:
turpentine
3
1a
:
3a
unknown amounts
Words
amount of
linseed oil +
amount of
turpentine
=
total amount
of polish
Let 1a = the amount of linseed oil.
Let 3a = the amount of turpentine.
Equation
1a
+
3a
=
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10
COURSE 3 LESSON 5-3
Write an Equation
(continued)
a + 3a = 10
4a = 10
4a 10
=
4
4
a = 2.5
Write the equation.
Combine like terms.
Divide each side by 4.
Simplify.
1(2.5) = 2.5
Substitute 2.5 for a in 1a.
The amount of linseed oil needed is 2.5 cups.
The amount of turpentine needed is 3(2.5) = 7.5. Since 7.5 + 2.5 = 10, the
answer is correct.
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COURSE 3 LESSON 5-3
Write an Equation
To paint a cabinet purple, you are going to mix red,
blue, and white paint in a ratio of 3 : 5 : 8. To make a gallon
of paint, how many ounces of each color will you use?
A gallon is 128 oz. The ratio of the paint colors is 3 to 5 to 8. Find how many
ounces of each color are needed.
Writing an equation will help you solve the problem. The ratio of red
to blue to white paint is 3 : 5 : 8. So 3p represents red, 5p represents blue,
and 8p represents white.
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COURSE 3 LESSON 5-3
Write an Equation
(continued)
Words
amount
of red +
5p
+
amount
of white
=
+
8p
=
Equation
3p
16p = 128
Combine like terms
16p 128
=
16
16
Divide each side by 16.
p=8
+
amount
of blue
Simplify.
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total amount of
paint needed
128
COURSE 3 LESSON 5-3
Write an Equation
(continued)
Substitute 8 for p in the expression for each color.
red: 3(8) = 24 oz blue: 5(8) = 40 oz white: 8(8) = 64 oz
Since 24 + 40 + 64 = 128, the answer is correct.
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COURSE 3 LESSON 5-3
Write an Equation
Write an equation to solve each problem. Show your equation and your
answer.
1. A punch recipe calls for 3.5 qt fruit juice to 2.5 qt soda water. You want
18 qt of punch in all. How much fruit juice do you need?
3.5x + 2.5x = 18; 10.5 qt
2. A painter is mixing white, yellow, and red in a ratio of 4 : 3 : 1. He
needs 2 gallons. If there are 128 ounces in a gallon, how much white
is needed?
4p + 3p + p = 2(128); 128 oz, or 1 gal
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