Math Practice Problems - Algebraic Sentences

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Algebraic Sentences - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=1, Mode=eqn

Write an algebraic expression or equation you would use to solve the situation given.

Complexity=2, Mode=eqn

Write an algebraic equation that represents the situation given.

Answers

Complexity=1, Mode=exp

Write an algebraic sentence using the given information. Use / for division. If money is involved, do not put $ in your answer.

Problem

Correct Answer

Your Answer

Tiffany is one-seventh as old as Cindy.
If Cindy is c years old, how old is Tiffany?

Solution

Tiffany	is	one-seventh	as old as	Cindy
Tiffany	=	¹ / ₇	×	c

This simplifies to ^c/₇

Problem

Correct Answer

Your Answer

Jose is 6 times as old as Sharon.
If Sharon is s years old, how old is Jose?

Solution

Jose	is	6 times	as old as	Sharon
Jose	=	6	×	s

This simplifies to 6s

Complexity=1, Mode=eqn

Write an algebraic expression or equation you would use to solve the situation given.

Problem

Correct Answer

Your Answer

Let Peter be p years old.
Cindy is one-tenth as old as Peter.
Cindy is 8 years old.
Focusing on the second sentence, write an equation that also incorporates information from the other sentences.

Solution

Cindy	is	one-tenth	as old as	Peter
8	=	¹ / ₁₀	×	p

This simplifies to ^p/₁₀ = 8

Problem

Correct Answer

Your Answer

Let f be the number of cookies.
There are one-eighth as many cupcakes as cookies on a tray.
There are 5 cupcakes.
Focusing on the second sentence, write an equation that also incorporates information from the other sentences.

Solution
"Let f be the number of cookies.
There are one-eighth as many cupcakes as cookies on a tray." means

Number of cupcakes	is	one-eighth	the number of cookies
5	=	¹/ ₈ ×	f

This simplifies to ^f/₈ = 5

Complexity=2, Mode=eqn

Write an algebraic equation that represents the situation given.

Problem

Correct Answer

Your Answer

The number of cats ( c ) is 8 fewer than 4 times the number of horses ( h ).

Solution

Number of cats	is	8 fewer	than	4 times the number of horses
c	=	- 8	+	4 × h

This simplifies to c = 4h - 8

Problem

Correct Answer

Your Answer

The number of cucumbers ( c ) is 10 more than 7 times the number of bell peppers ( b ).

Solution

Number of cucumbers	is	10 more	than	7 times the number of bell peppers
c	=	+ 10	+	7 × b

This simplifies to c = 7b + 10

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