1-2 Variables and Expressions
Translate each phrase into an algebraic expression.
12. three times as many balloons
SOLUTION: Let b represent the number of balloons. The word “times” indicates multiplication. So, the phrase three times as
many balloons can be translated into the algebraic expression 3b.
13. twenty-four pieces of candy divided among some students
SOLUTION: Let s represent the number of students. The words “divided among” indicate division. So, the phrase twenty-four
pieces of candy divided among some students can be translated into the algebraic expression 24 ÷ s.
14. the number of people increased by thirteen
SOLUTION: Let p represent the number of people. The words “increased by” indicate addition. So, the phrase the number of
people increased by thirteen can be translated into the algebraic expression p + 13.
15. the number of inches in any number of feet
SOLUTION: Let n represent the number of feet. The words “the number in some” indicate multiplication. So, the phrase the
number of inches in some feet can be translated into the algebraic expression 12n.
16. four more than the number of weeks in a group of days
SOLUTION: Let n represent the number of days. The words “number in a group of” indicates division. Since there are seven
days in a week, the algebraic expression
gives the number of weeks in a group of n days. The words “more
than” indicate addition. So, the phrase four more than the number of weeks in a group of days can be translated
into the algebraic expression
.
17. four less than the amount of cents in a number of dimes
SOLUTION: Let n represent the number of dimes. The words “amount in a number of” indicates multiplication. Since a dime is
worth 10 cents, the algebraic expression 10n gives the number of cents in a group of n dimes. The words “less than”
indicates subtraction. So, the phrase four less than the amount of cents in a number of dimes can be translated
into the algebraic expression 10n – 4.
ALGEBRA Evaluate each expression if a = 9, b = 4, and c = 11.
18. b + 9
SOLUTION: 19. 13 – a
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SOLUTION: 1-2 Variables and Expressions
19. 13 – a
SOLUTION: 20. 2c – 5
SOLUTION: 21. 18 + 4b
SOLUTION: 22. SOLUTION: 23. SOLUTION: 24. 5c – 4a
SOLUTION: 25. 7b – 2c
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SOLUTION: 1-2 Variables and Expressions
25. 7b – 2c
SOLUTION: 26. SOLUTION: 27. SOLUTION: 28. 4b + 3c – 5a
SOLUTION: 29. 6c – 2a + 6b
SOLUTION: 30. PHOTOGRAPHY A studio charges a sitting fee of $25 plus $7 for each portrait sheet ordered. Write an
expression that can be used to find the total cost to have photographs taken. Then find the cost of purchasing twelve
portrait sheets.
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Let s represent a portrait sheet. The word “plus” indicates addition. So, the phrase a sitting fee of $25 plus $7 for
each portrait sheet ordered can be translated into the algebraic expression 25 + 7s. To find the cost of purchasing
1-2 Variables and Expressions
30. PHOTOGRAPHY A studio charges a sitting fee of $25 plus $7 for each portrait sheet ordered. Write an
expression that can be used to find the total cost to have photographs taken. Then find the cost of purchasing twelve
portrait sheets.
SOLUTION: Let s represent a portrait sheet. The word “plus” indicates addition. So, the phrase a sitting fee of $25 plus $7 for
each portrait sheet ordered can be translated into the algebraic expression 25 + 7s. To find the cost of purchasing
12 portrait sheets, replace the s with 12 in the expression 25 + 7s.
So, the cost of purchasing twelve portrait sheets is $109.
31. MEASUREMENT One gallon of water is equal to 231 cubic inches. Write an expression for the number of gallons
of water in any number of cubic inches of water.
SOLUTION: Let w represent the number of cubic inches of water. Since one gallon of water is equal to 231 cubic inches, divide
the number of cubic inches of water by 231 to find the number of gallons of water. So, the expression
can be used to find the number of gallons of water in any number of cubic inches of water.
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