## 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=exp

Write an algebraic sentence using the given information. Use / for division.
 1.   It costs r dollars for 2 pounds of grapes. How much does each pound of grapes cost? 2.   There are one-eighth as many grapes as melons on a table.If there are m melons, how many grapes are there?

### Complexity=1, Mode=eqn

Write an algebraic equation you would use to solve the situation given. Order by magnitude and put the variables on the left side. For example, write 2s+4=12, not 12=4+2s.
 1.   There are half as many zebras as monkeys in a zoo.There are 2 zebras. Let m be the number of monkeys. 2.   There are 8 more cats than ducks in a barn.There are 56 cats. Let d be the number of ducks.

### Complexity=2, Mode=eqn

Write an algebraic equation that represents the situation given.
 1.   To rent a boat, there is a fee of \$24 plus an hourly rate of \$5 per hour. Peter spent \$39 to rent a boat for w hours. 2.   Tiffany is 5 years older than 6 times Sharon's age ( s ).Tiffany is t years old.

### Complexity=1, Mode=exp

Write an algebraic sentence using the given information. Use / for division.
1It costs r dollars for 2 pounds of grapes.
How much does each pound of grapes cost?

Solution
 Unit cost = Total cost ÷ Number of items = r ÷ 2

This simplifies to   r/2
2There are one-eighth as many grapes as melons on a table.
If there are m melons, how many grapes are there?

Solution
"There are one-eighth as many grapes as melons on a table." means
 Number of grapes is one-eighth the number of melons = 1/ 8   × m

This simplifies to   m / 8

### Complexity=1, Mode=eqn

Write an algebraic equation you would use to solve the situation given. Order by magnitude and put the variables on the left side. For example, write 2s+4=12, not 12=4+2s.
1There are half as many zebras as monkeys in a zoo.
There are 2 zebras. Let m be the number of monkeys.

Solution
"There are half as many zebras as monkeys in a zoo." means
 Number of zebras is half the number of monkeys 2 = 1/ 2   × m

This simplifies to   m / 2 = 2
2There are 8 more cats than ducks in a barn.
There are 56 cats. Let d be the number of ducks.

Solution
"There are 8 more cats than ducks in a barn." means
 Number of cats is 8 more than the number of ducks 56 = + 8 + d

This simplifies to   d + 8 = 56

### Complexity=2, Mode=eqn

Write an algebraic equation that represents the situation given.
1To rent a boat, there is a fee of \$24 plus an hourly rate of \$5 per hour.
Peter spent \$39 to rent a boat for w hours.

Solution
 Total cost = Initial fee + Hourly rate × Number of hours 39 = 24 + 5 × w

This simplifies to   5w + 24 = 39