Virginia SOL Grade 7 Math Word Problems and Mixed Practice

Grade 7 SOL math word problems require students to translate a real situation into math, choose an efficient strategy, and check whether the answer makes sense. The strongest review plan includes proportional reasoning, rational number operations, equations, geometry, probability, and data analysis in the same practice session.

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How to Use This Mixed Practice Set

Have students solve the problems independently first. Then review the answer key and sort mistakes by topic. A missed ratio question and a missed equation question should lead to different reteaching plans.

Grade 7 SOL Word Problems

Ratios and Proportional Reasoning

1. A car travels 189 miles in 3 hours at a constant speed. How far will it travel in 5 hours at the same speed?
2. A map scale says 1 inch represents 24 miles. Two towns are 3.5 inches apart on the map. What is the actual distance between the towns?
3. A smoothie recipe uses 2 cups of yogurt for every 5 cups of fruit. How many cups of fruit are needed if the recipe uses 6 cups of yogurt?

Rational Numbers and Percents

4. The temperature was -6 degrees at sunrise. It rose 18 degrees by noon and dropped 7 degrees by evening. What was the evening temperature?
5. A jacket costs $80. It is discounted by 25%. What is the sale price?
6. A student answered 34 out of 40 questions correctly. What percent of the questions were correct?

Expressions and Equations

7. Solve: 5x – 8 = 27.
8. A taxi charges a $4 starting fee plus $2.50 per mile. Write an expression for the cost of m miles. What is the cost for 6 miles?
9. Maya earns $14 per hour and receives a one-time bonus of $18. If she earns $116 total, how many hours did she work?

Geometry and Measurement

10. A triangle has a base of 16 inches and a height of 9 inches. What is its area?
11. A rectangular prism is 8 cm long, 5 cm wide, and 4 cm high. What is the volume?
12. A circle has a radius of 6 meters. Using 3.14 for pi, what is its circumference?

Probability and Statistics

13. A bag contains 5 red marbles, 3 blue marbles, and 4 green marbles. What is the probability of choosing a green marble?
14. The data set is 8, 10, 10, 13, 14, 25. Find the median and identify whether the data set has an outlier.
15. A spinner has 8 equal sections: 3 red, 2 blue, 2 yellow, and 1 green. What is the probability of landing on red or yellow?

Answer Key with Explanations

1. 63 miles per hour; 63 x 5 = 315 miles.
2. 3.5 x 24 = 84 miles.
3. The yogurt is tripled from 2 to 6, so fruit is 5 x 3 = 15 cups.
4. -6 + 18 = 12; 12 – 7 = 5 degrees.
5. 25% of $80 is $20; $80 – $20 = $60.
6. 34/40 = 0.85 = 85%.
7. 5x = 35, so x = 7.
8. Expression: 4 + 2.50m. For 6 miles: 4 + 15 = $19.
9. 14h + 18 = 116; 14h = 98; h = 7 hours.
10. Area = 1/2 x 16 x 9 = 72 square inches.
11. Volume = 8 x 5 x 4 = 160 cubic centimeters.
12. Circumference = 2 x 3.14 x 6 = 37.68 meters.
13. There are 12 marbles total; probability = 4/12 = 1/3.
14. Median = (10 + 13)/2 = 11.5. The value 25 is a likely outlier compared with the rest of the data.
15. Red or yellow sections = 3 + 2 = 5, so probability = 5/8.

Five More Mixed Word Problems

16. A school orders 18 boxes of notebooks. Each box has 24 notebooks. The notebooks are shared equally among 12 classrooms. How many notebooks does each classroom receive?
17. A recipe uses 3/4 cup of sugar. Lena makes 2 1/2 batches. How many cups of sugar does she need?
18. The expression 9.50h + 12 represents the cost, in dollars, of renting a bike for h hours plus a helmet fee. What is the cost for 4 hours?
19. A cylinder-shaped can has a diameter of 10 cm and a height of 12 cm. Using 3.14 for pi, what is the volume?
20. The scores on a quiz are 72, 78, 81, 85, 89, and 99. Which measure, mean or median, better represents a typical score if the teacher thinks 99 is unusually high? Explain.

Worked Answers for the Extra Problems

16. 18 x 24 = 432 notebooks. Then 432 / 12 = 36 notebooks per classroom.
17. 2 1/2 = 5/2. Then 3/4 x 5/2 = 15/8 = 1 7/8 cups.
18. 9.50 x 4 + 12 = 38 + 12 = $50.
19. The radius is 5 cm. Volume = pi x r^2 x h = 3.14 x 25 x 12 = 942 cubic centimeters.
20. The median may be better because 99 pulls the mean upward. Median = (81 + 85) / 2 = 83.

Common SOL Word-Problem Habits

• Underline the question. Many wrong answers are correct calculations for the wrong quantity.
• Write units in the setup. Miles, dollars, square inches, and cubic centimeters point to different operations.
• Estimate before solving. A 25% discount from $80 should be near $60, not $20 or $100.
• Check proportional problems with a table. Ratio tables prevent students from adding when they should multiply.
• Review wrong answers by topic. Mixed practice only helps if students use the results to choose the next review skill.

What Each Mistake Should Trigger Next

If a student misses a proportional reasoning problem, have them build a ratio table before trying another problem. If they miss a percent question, ask them to write the percent as a decimal and estimate the answer before calculating. If they miss an equation problem, have them define the variable in words first. If they miss geometry, require a labeled sketch with units. If they miss statistics, ask whether the question is about center, spread, or probability before any computation starts.

A good Grade 7 SOL review week includes two focused skill days, one mixed word-problem day, one correction day, and one short timed set. The correction day matters most: students should rewrite missed problems with a new sentence explaining the strategy. That is where word-problem practice turns into durable skill.

Virginia Grade 7 SOL Practice Resources

ViewMath Virginia SOL Grade 7 books provide state-specific study guides, workbooks, and practice tests with answer explanations. Use the sidebar recommendations when students need more mixed practice after this word-problem set.