## Algebraic Sentences 2 - 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=basic

Write an algebraic sentence using the given information. Use / for division.
Use <= for ≤ and >= for ≥
 1.   Peter earns at least 8 dollars an hour. Let p be what Peter earns hourly. 2.   John earns at least 10 dollars an hour. Let j be what John earns hourly.

### Complexity=1, Mode=avg

Write an algebraic sentence using the given information. Use / for division.
Use <= for ≤ and >= for ≥
1.   One-tenth of a number ( f ) is at most -7. 2.   You score 14, 20, and 27 points in your first 3 games.
Your goal is to have an average of at least 23 points per game.
Let z = number of points you score in the next game. Which inequality matches your goal?

Use <= for ≤ and >= for ≥
 1.   Let a be the number of adults on a bus.  What does 6(a + 10) represent?        16 more than the number of adults on a bus        6 times the number of adults on another bus that has 10 more adults        60 more than the number of adults on a bus        10 more than 6 times the number of adults on a bus 2.   Express the following relationship as an algebraic sentence. (Do not include dollar signs, \$, in your answer.) The cost of buying DVD's online is \$10 per DVD plus \$19 for shipping.  You don't want your spending to exceed \$55.  Let z = number of DVD's you can purchase.

### Complexity=1, Mode=basic

Write an algebraic sentence using the given information. Use / for division.
Use <= for ≤ and >= for ≥
1Peter earns at least 8 dollars an hour.
Let p be what Peter earns hourly.

Solution
At least 8 means 8 or more which mathematically is greater than or equal to 8.
2John earns at least 10 dollars an hour.
Let j be what John earns hourly.

Solution
At least 10 means 10 or more which mathematically is greater than or equal to 10.

### Complexity=1, Mode=avg

Write an algebraic sentence using the given information. Use / for division.
Use <= for ≤ and >= for ≥
1One-tenth of a number ( f ) is at most -7.
Solution
At most -7 means -7 or less which mathematically is less than or equal to -7.
2You score 14, 20, and 27 points in your first 3 games.
Your goal is to have an average of at least 23 points per game.
Let z = number of points you score in the next game. Which inequality matches your goal?
Solution

Use <= for ≤ and >= for ≥
1Let a be the number of adults on a bus.  What does 6(a + 10) represent?        16 more than the number of adults on a bus
6 times the number of adults on another bus that has 10 more adults
60 more than the number of adults on a bus
10 more than 6 times the number of adults on a bus
Solution
16 more than the number of adults on a bus
a + (6 + 10)
6 times the number of adults on another bus that has 10 more adults
6(a + 10)
60 more than the number of adults on a bus
a + (6 × 10)
10 more than 6 times the number of adults on a bus
6a + 10
2Express the following relationship as an algebraic sentence.