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## 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

Solve. When writing an algebraic sentence, type <= and >= for ≤ and ≥.

 1.   Let m be what Miguel earns hourly. Miguel earns at least 8 dollars an hour. 2.   Let j be what Jose earns hourly. Jose earns more than 14 dollars an hour.

### Complexity=1, Mode=avg

Solve. When writing an algebraic sentence, type <= and >= for ≤ and ≥. Use / for division.

 1.   One-third of a number ( t ) is more than -6. 2.   The sum of two consecutive odd integers is at most 20. Let e = the smaller integer. Which inequality matches this situation?        e + e ≤ 20        e + (e + 1) ≤ 20        e + (e + 1) ≥ 20        e + e ≥ 20        e + (e + 2) ≥ 20        e + (e + 2) ≤ 20

Solve. When writing an algebraic sentence, type <= and >= for ≤ and ≥. Use / for division.

 1.   Express the following relationship as an algebraic sentence. (Do not include dollar signs, \$, in your answer.) The cost of buying books online is \$8 per book plus \$16 for shipping.  You don't want your spending to exceed \$42.  Let c = number of books you can purchase. 2.   Let p be the number of pies on a tray.  What does 2p - 4 represent?        4 less than twice the number of pies on a tray        Twice the number of pies on another tray that has 4 fewer pies        Twice the number of pies on another tray that has 4 more pies        4 less than 2 pies on a tray        4 more than twice the number of pies on a tray        4 more than 2 pies on a tray

### Complexity=1, Mode=basic

Solve. When writing an algebraic sentence, type <= and >= for ≤ and ≥.

1Let m be what Miguel earns hourly.
Miguel earns at least 8 dollars an hour.

Solution
At least 8 means 8 or more which mathematically is greater than or equal to 8.
2Let j be what Jose earns hourly.
Jose earns more than 14 dollars an hour.

Solution
More than 14 means greater than 14.

### Complexity=1, Mode=avg

Solve. When writing an algebraic sentence, type <= and >= for ≤ and ≥. Use / for division.

1One-third of a number ( t ) is more than -6.
2The sum of two consecutive odd integers is at most 20.
Let e = the smaller integer. Which inequality matches this situation?
e + e ≤ 20
e + (e + 1) ≤ 20
e + (e + 1) ≥ 20
e + e ≥ 20
e + (e + 2) ≥ 20
e + (e + 2) ≤ 20
Solution
Consecutive odd integers are 2 apart.
When e is the smaller integer, the next odd integer is e + 2.

Solve. When writing an algebraic sentence, type <= and >= for ≤ and ≥. Use / for division.

1Express the following relationship as an algebraic sentence.

The cost of buying books online is \$8 per book plus \$16 for shipping.  You
don't want your spending to exceed \$42.  Let c = number of books
you can purchase.

Solution
To not exceed means to not go beyond, or mathematically, less than or equal to.
To exceed means greater than.
2Let p be the number of pies on a tray.  What does 2p - 4 represent?
4 less than twice the number of pies on a tray
Twice the number of pies on another tray that has 4 fewer pies
Twice the number of pies on another tray that has 4 more pies
4 less than 2 pies on a tray
4 more than twice the number of pies on a tray
4 more than 2 pies on a tray
Solution
There are the meanings of the answer choices:
4 less than twice the number of pies on a tray
2p - 4

Twice the number of pies on another tray that has 4 fewer pies
2(p - 4)
Twice the number of pies on another tray that has 4 more pies
2(p + 4)
4 less than 2 pies on a tray
2 - 4
4 more than twice the number of pies on a tray
2p + 4
4 more than 2 pies on a tray
2 + 4   