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Translate and solve: The number 143 is the product of and y .
Begin by translating the sentence into an equation.
Translate. |
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Divide by . |
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Simplify. |
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Check:
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Translate and solve: The number 132 is the product of −12 and y .
Translate and solve: The number 117 is the product of −13 and z .
Translate and solve: divided by 8 is .
Begin by translating the sentence into an equation.
Translate. |
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Multiple both sides by 8. |
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Simplify. |
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Check: | Is divided by 8 equal to −32? | |
Let . | Is divided by equal to ? | |
Translate. | ||
Simplify. |
Translate and solve: The quotient of and is .
Begin by translating the sentence into an equation.
Translate. |
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Multiply both sides by . |
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Simplify. |
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Check: | Is the quotient of and equal to ? | |
Let . | Is the quotient of and equal to ? | |
Translate. | ||
Simplify. |
Translate and solve: Three-fourths of is 18.
Begin by translating the sentence into an equation. Remember, “of” translates into multiplication.
Translate. |
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Multiply both sides by |
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Simplify. |
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Check: | Is three-fourths of p equal to 18? | |
Let | Is three-fourths of 24 equal to 18? | |
Translate. | ||
Simplify. |
Translate and solve: The sum of three-eighths and is one-half.
Begin by translating the sentence into an equation.
Translate. |
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Subtract from each side. |
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Simplify and rewrite fractions with common denominators. |
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Simplify. |
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Check: | Is the sum of three-eighths and equal to one-half? | ||
Is the sum of three-eighths and one-eighth equal to one-half? | |||
Translate. | |||
Simplify. | |||
Simplify. |
Translate and solve: The sum of five-eighths and x is one-fourth.
Translate and solve: The sum of three-fourths and x is five-sixths.
To solve applications using the Division and Multiplication Properties of Equality, we will follow the same steps we used in the last section. We will restate the problem in just one sentence, assign a variable, and then translate the sentence into an equation to solve.
Denae bought 6 pounds of grapes for $10.74. What was the cost of one pound of grapes?
Translate and solve:
Arianna bought a 24-pack of water bottles for $9.36. What was the cost of one water bottle?
$0.39
Translate and solve:
At JB’s Bowling Alley, 6 people can play on one lane for $34.98. What is the cost for each person?
$5.83
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