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Algebra Word Problems Practice Tests

These Grade 9 Math practice tests cover consecutive numbers, ages and averages, rates and distance, travel, money and percentages, tickets, commissions, interest, geometry, work rates, mixtures, growth, break-even models, and fixed-plus-variable costs.

Skills covered

  • Defining variables and translating words into equations
  • Solving number, average, rate, distance, and work problems
  • Modeling discounts, tax, tips, commissions, interest, tickets, and budgets
  • Using perimeter, area, volume, circles, triangles, and the Pythagorean theorem
  • Interpreting mixtures, percentages, growth, break-even points, and real-world units

How to use these practice tests

Read the question for quantities and units, define one unknown, write a relationship, solve step by step, and reject values that do not fit the situation. Include units in the final answer.

For more Grade 9 Math practice, return to the Grade 9 Math category.

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5. Test

Grade 9 Algebra Word Problems Practice Tests

Practice Grade 9 Math questions about number problems, rates, distance, money, percentages, tickets, geometry, work, mixtures, growth, and algebraic models.

Choose the best answer. Define the unknown, write an equation or model, keep units consistent, solve, and check that the result makes sense in context.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

Two pounds of a $3-per-pound ingredient and three pounds of a $5-per-pound ingredient cost how much?

Please select an answer first.

Correct answer: A

The correct answer is $21.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: The total is 2(3) + 3(5) = 6 + 15 = 21 dollars.
  3. Check the context: The correct choice is $21.

The total is 2(3) + 3(5) = 6 + 15 = 21 dollars.

2. QuestionMultiple choice

A recipe uses 2 cups of flour for every 3 batches. How much flour is needed for 12 batches?

Please select an answer first.

Correct answer: B

The correct answer is 8 cups.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: The scale factor is 12/3 = 4, so flour needed is 2 × 4 = 8 cups.
  3. Check the context: The correct choice is 8 cups.

The scale factor is 12/3 = 4, so flour needed is 2 × 4 = 8 cups.

3. QuestionMultiple choice

A mixture contains 4 cups of juice and 2 cups of water. What fraction of the mixture is juice?

Please select an answer first.

Correct answer: C

The correct answer is 23\frac{2}{3}.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: There are 6 cups total, so the juice fraction is 4/6 = 2/3.
  3. Check the context: The correct choice is 23\frac{2}{3}.

There are 6 cups total, so the juice fraction is 4/6 = 2/3.

4. QuestionMultiple choice

One worker completes a job in 6 hours and another in 3 hours. How long would they take together?

Please select an answer first.

Correct answer: D

The correct answer is 2 hours.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Their combined rate is 1/6 + 1/3 = 1/2 job per hour, so the time is 2 hours.
  3. Check the context: The correct choice is 2 hours.

Their combined rate is 1/6 + 1/3 = 1/2 job per hour, so the time is 2 hours.

5. QuestionMultiple choice

A population of 1,200 decreases by 5%. What is the new population?

Please select an answer first.

Correct answer: A

The correct answer is 1,140.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: The decrease is 0.05 × 1,200 = 60, so the new population is 1,140.
  3. Check the context: The correct choice is 1,140.

The decrease is 0.05 × 1,200 = 60, so the new population is 1,140.

6. QuestionMultiple choice

The temperature is 68 degrees and increases by 10 degrees. What is the new temperature?

Please select an answer first.

Correct answer: B

The correct answer is 78 degrees.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Add the change to the starting value: 68 + 10 = 78 degrees.
  3. Check the context: The correct choice is 78 degrees.

Add the change to the starting value: 68 + 10 = 78 degrees.

7. QuestionMultiple choice

A machine worth $800 loses 15% of its value. What is its new value?

Please select an answer first.

Correct answer: C

The correct answer is $680.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: The loss is 0.15 × 800 = 120 dollars, so the value is 800 - 120 = 680 dollars.
  3. Check the context: The correct choice is $680.

The loss is 0.15 × 800 = 120 dollars, so the value is 800 - 120 = 680 dollars.

8. QuestionMultiple choice

A project starts with 50 points and gains 8 points each day. How many points are there after 7 days?

Please select an answer first.

Correct answer: D

The correct answer is 106.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Use 50 + 8(7) = 106 points.
  3. Check the context: The correct choice is 106.

Use 50 + 8(7) = 106 points.

9. QuestionMultiple choice

A business has cost C=100+4xC=100+4x and revenue R=9xR=9x. At what x-value is it at break-even?

Please select an answer first.

Correct answer: A

The correct answer is 20.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Set cost equal to revenue: 100 + 4x = 9x, so 100 = 5x and x = 20.
  3. Check the context: The correct choice is 20.

Set cost equal to revenue: 100 + 4x = 9x, so 100 = 5x and x = 20.

10. QuestionMultiple choice

Which equation models a $5 entry fee plus $2 for each of x games?

Please select an answer first.

Correct answer: B

The correct answer is C=5+2xC=5+2x.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: The fixed fee is 5 and the variable cost is 2 times the number of games.
  3. Check the context: The correct choice is C=5+2xC=5+2x.

The fixed fee is 5 and the variable cost is 2 times the number of games.

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