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Systems of Equations Word Problems — Easy Worksheet 2
Grade 8 · Whoobee Name: ____________________ Date: __________
Write a system of equations for each story, solve it, and answer the question with a number.
How to solve
Choose a variable for each unknown (for example a = adult tickets, c = child tickets). Write one equation for each fact in the story — usually one for the count and one for the total value. Solve by substitution or elimination and answer exactly what the question asks.
Example
A school play sold 56 tickets. Adult tickets cost $9 and child tickets cost $5. The play earned $388. How many adult tickets were sold?
Answer: 27
Not quite. The answer is
💡 Let a = adult tickets and c = child tickets. Count: a + c = 37. Money: 8a + 6c = 270. Multiply the first equation by 6: 6a + 6c = 222. Subtract it from the second: 2a = 48. Divide by 2: a = 24. Then c = 37 − 24 = 13. Check: 8 × 24 + 6 × 13 = 192 + 78 = 270. So 13 child tickets were sold.
✓ Correct!
Not quite. The answer is
💡 Let a = adult tickets and c = child tickets. Count: a + c = 37. Money: 8a + 6c = 270. Multiply the first equation by 6: 6a + 6c = 222. Subtract it from the second: 2a = 48. Divide by 2: a = 24. Then c = 37 − 24 = 13. Check: 8 × 24 + 6 × 13 = 192 + 78 = 270. So 13 child tickets were sold.
💡 How to solve: Systems of Equations Word Problems
Choose a variable for each unknown (for example a = adult tickets, c = child tickets). Write one equation for each fact in the story — usually one for the count and one for the total value. Solve by substitution or elimination and answer exactly what the question asks.
Try a similar one
The sum of two numbers is 34 and their difference is 2. What is the smaller number?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Let a = adult tickets and c = child tickets. Count: a + c = 41. Money: 14a + 5c = 358. Multiply the first equation by 5: 5a + 5c = 205. Subtract it from the second: 9a = 153. Divide by 9: a = 17. Then c = 41 − 17 = 24. Check: 14 × 17 + 5 × 24 = 238 + 120 = 358. So 24 child tickets were sold.
✓ Correct!
Not quite. The answer is
💡 Let a = adult tickets and c = child tickets. Count: a + c = 41. Money: 14a + 5c = 358. Multiply the first equation by 5: 5a + 5c = 205. Subtract it from the second: 9a = 153. Divide by 9: a = 17. Then c = 41 − 17 = 24. Check: 14 × 17 + 5 × 24 = 238 + 120 = 358. So 24 child tickets were sold.
💡 How to solve: Systems of Equations Word Problems
Choose a variable for each unknown (for example a = adult tickets, c = child tickets). Write one equation for each fact in the story — usually one for the count and one for the total value. Solve by substitution or elimination and answer exactly what the question asks.
Try a similar one
Mia has 22 coins, all dimes and quarters, worth $4.45 in total. How many quarters does she have?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Let f = 5-point questions and t = 2-point questions. Questions: f + t = 24. Points: 5f + 2t = 69. Multiply the first equation by 2: 2f + 2t = 48. Subtract it from the second: 3f = 21. Divide by 3: f = 7. Then t = 24 − 7 = 17. Check: 5 × 7 + 2 × 17 = 35 + 34 = 69. So 7 questions are worth 5 points.
✓ Correct!
Not quite. The answer is
💡 Let f = 5-point questions and t = 2-point questions. Questions: f + t = 24. Points: 5f + 2t = 69. Multiply the first equation by 2: 2f + 2t = 48. Subtract it from the second: 3f = 21. Divide by 3: f = 7. Then t = 24 − 7 = 17. Check: 5 × 7 + 2 × 17 = 35 + 34 = 69. So 7 questions are worth 5 points.
💡 How to solve: Systems of Equations Word Problems
Choose a variable for each unknown (for example a = adult tickets, c = child tickets). Write one equation for each fact in the story — usually one for the count and one for the total value. Solve by substitution or elimination and answer exactly what the question asks.
Try a similar one
Mia has 26 coins, all dimes and quarters, worth $4.55 in total. How many quarters does she have?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Let x = the larger number and y = the smaller number. x + y = 37 and x − y = 21. Add the equations to get rid of y: 2x = 58, so x = 29. Then y = 37 − 29 = 8. Check: 29 − 8 = 21. The smaller number is 8.
✓ Correct!
Not quite. The answer is
💡 Let x = the larger number and y = the smaller number. x + y = 37 and x − y = 21. Add the equations to get rid of y: 2x = 58, so x = 29. Then y = 37 − 29 = 8. Check: 29 − 8 = 21. The smaller number is 8.
💡 How to solve: Systems of Equations Word Problems
Choose a variable for each unknown (for example a = adult tickets, c = child tickets). Write one equation for each fact in the story — usually one for the count and one for the total value. Solve by substitution or elimination and answer exactly what the question asks.
Try a similar one
A school play sold 49 tickets. Adult tickets cost $12 and child tickets cost $5. The play earned $322. How many child tickets were sold?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Let w = cows and c = chickens. Heads: w + c = 26. Legs: 4w + 2c = 66. Multiply the first equation by 2: 2w + 2c = 52. Subtract it from the second: 2w = 14. Divide by 2: w = 7. Then c = 26 − 7 = 19. Check: 4 × 7 + 2 × 19 = 28 + 38 = 66. So there are 7 cows on the farm.
✓ Correct!
Not quite. The answer is
💡 Let w = cows and c = chickens. Heads: w + c = 26. Legs: 4w + 2c = 66. Multiply the first equation by 2: 2w + 2c = 52. Subtract it from the second: 2w = 14. Divide by 2: w = 7. Then c = 26 − 7 = 19. Check: 4 × 7 + 2 × 19 = 28 + 38 = 66. So there are 7 cows on the farm.
💡 How to solve: Systems of Equations Word Problems
Choose a variable for each unknown (for example a = adult tickets, c = child tickets). Write one equation for each fact in the story — usually one for the count and one for the total value. Solve by substitution or elimination and answer exactly what the question asks.
Try a similar one
A school play sold 39 tickets. Adult tickets cost $13 and child tickets cost $10. The play earned $462. How many child tickets were sold?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Let m = the number of months and y = the cost in dollars. Gym A: y = 32m + 33. Gym B: y = 27m + 58. Set the costs equal: 32m + 33 = 27m + 58. Subtract 27m from both sides: 5m + 33 = 58. Subtract 33: 5m = 25. Divide by 5: m = 5. Check: Gym A costs 33 + 32 × 5 = 193 and Gym B costs 58 + 27 × 5 = 193. They cost the same after 5 months.
✓ Correct!
Not quite. The answer is
💡 Let m = the number of months and y = the cost in dollars. Gym A: y = 32m + 33. Gym B: y = 27m + 58. Set the costs equal: 32m + 33 = 27m + 58. Subtract 27m from both sides: 5m + 33 = 58. Subtract 33: 5m = 25. Divide by 5: m = 5. Check: Gym A costs 33 + 32 × 5 = 193 and Gym B costs 58 + 27 × 5 = 193. They cost the same after 5 months.
💡 How to solve: Systems of Equations Word Problems
Choose a variable for each unknown (for example a = adult tickets, c = child tickets). Write one equation for each fact in the story — usually one for the count and one for the total value. Solve by substitution or elimination and answer exactly what the question asks.
Try a similar one
A test has 11 questions worth 37 points in all. Some questions are worth 2 points and the rest are worth 5 points. How many 5-point questions are on the test?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Work in cents: $4.45 = 445 cents. Let q = quarters and d = dimes. Coins: q + d = 22. Value: 25q + 10d = 445. Multiply the first equation by 10: 10q + 10d = 220. Subtract it from the second: 15q = 225. Divide by 15: q = 15. Then d = 22 − 15 = 7. Check: 25 × 15 + 10 × 7 = 375 + 70 = 445. So Mia has 15 quarters.
✓ Correct!
Not quite. The answer is
💡 Work in cents: $4.45 = 445 cents. Let q = quarters and d = dimes. Coins: q + d = 22. Value: 25q + 10d = 445. Multiply the first equation by 10: 10q + 10d = 220. Subtract it from the second: 15q = 225. Divide by 15: q = 15. Then d = 22 − 15 = 7. Check: 25 × 15 + 10 × 7 = 375 + 70 = 445. So Mia has 15 quarters.
💡 How to solve: Systems of Equations Word Problems
Choose a variable for each unknown (for example a = adult tickets, c = child tickets). Write one equation for each fact in the story — usually one for the count and one for the total value. Solve by substitution or elimination and answer exactly what the question asks.
Try a similar one
The sum of two numbers is 40 and their difference is 18. What is the smaller number?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Let x = the larger number and y = the smaller number. x + y = 12 and x − y = 4. Add the equations to get rid of y: 2x = 16, so x = 8. Then y = 12 − 8 = 4. Check: 8 − 4 = 4. The smaller number is 4.
✓ Correct!
Not quite. The answer is
💡 Let x = the larger number and y = the smaller number. x + y = 12 and x − y = 4. Add the equations to get rid of y: 2x = 16, so x = 8. Then y = 12 − 8 = 4. Check: 8 − 4 = 4. The smaller number is 4.
💡 How to solve: Systems of Equations Word Problems
Choose a variable for each unknown (for example a = adult tickets, c = child tickets). Write one equation for each fact in the story — usually one for the count and one for the total value. Solve by substitution or elimination and answer exactly what the question asks.
Try a similar one
A school play sold 39 tickets. Adult tickets cost $8 and child tickets cost $5. The play earned $225. How many child tickets were sold?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Systems of Equations Word Problems — Easy Worksheet 2
Write a system of equations for each story, solve it, and answer the question with a number.