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Grade 8 Quiz: Word Problems — Easy Version 2
Grade 8 · MathSheets Name: ____________________ Date: __________
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.
How to solve
This quiz mixes questions from different lessons, like a real test. Read each question carefully: the lesson name in front tells you what kind of problem it is. Check your answers, then practise the lessons where you made mistakes.
Example
Word Problems: The sum of three consecutive whole numbers is 9. What is the smallest of the three numbers?
Answer: 2
Not quite. The answer is
💡 Let m = the number of months. The sign-up fee plus the monthly cost makes what she paid: 40 + 10m = 100. Subtract 40 from both sides: 10m = 60. Divide both sides by 10: m = 6. Check: 40 + 10 × 6 = 100. She has been a member for 6 months.
✓ Correct!
Not quite. The answer is
💡 Let m = the number of months. The sign-up fee plus the monthly cost makes what she paid: 40 + 10m = 100. Subtract 40 from both sides: 10m = 60. Divide both sides by 10: m = 6. Check: 40 + 10 × 6 = 100. She has been a member for 6 months.
💡 How to solve: Word Problems
Set up the equation total = flat fee + (cost per mile × miles). Subtract the flat fee from the total, then divide by the cost per mile to find the number of miles.
Try a similar one
The sum of three consecutive whole numbers is 21. What is the smallest of the three numbers?
✓ 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
💡 The width, the height and the diagonal make a right triangle, and the diagonal is the hypotenuse. c2 = 122 + 162 = 144 + 256 = 400, so c = √400 = 20. The diagonal is 20 inches long.
✓ Correct!
Not quite. The answer is
💡 The width, the height and the diagonal make a right triangle, and the diagonal is the hypotenuse. c2 = 122 + 162 = 144 + 256 = 400, so c = √400 = 20. The diagonal is 20 inches long.
💡 How to solve: Pythagorean Theorem: Missing Legs & Word Problems
In a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. To find a missing leg, subtract: b2 = c2 - a2, then take the square root. For the diagonal of a box, first find the diagonal of the base, then use it as a leg with the height: d2 = l2 + w2 + h2.
Try a similar one
A right triangle has a leg of 9 and a hypotenuse of 15. Find the other leg.
✓ 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 = 20 and x − y = 4. Add the equations to get rid of y: 2x = 24, so x = 12. Then y = 20 − 12 = 8. Check: 12 − 8 = 4. The smaller number is 8.
✓ Correct!
Not quite. The answer is
💡 Let x = the larger number and y = the smaller number. x + y = 20 and x − y = 4. Add the equations to get rid of y: 2x = 24, so x = 12. Then y = 20 − 12 = 8. Check: 12 − 8 = 4. 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
Gym A charges a $49 joining fee plus $26 per month. Gym B charges a $115 joining fee plus $15 per month. After how many months do the two gyms cost the same?
✓ 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 = the width; the length is w + 12. Perimeter = 2 × width + 2 × length: 2w + 2(w + 12) = 40, so 4w + 24 = 40. Subtract 24 from both sides: 4w = 16. Divide both sides by 4: w = 4. Check: 4 × 4 + 24 = 40. The rectangle is 4 cm wide.
✓ Correct!
Not quite. The answer is
💡 Let w = the width; the length is w + 12. Perimeter = 2 × width + 2 × length: 2w + 2(w + 12) = 40, so 4w + 24 = 40. Subtract 24 from both sides: 4w = 16. Divide both sides by 4: w = 4. Check: 4 × 4 + 24 = 40. The rectangle is 4 cm wide.
💡 How to solve: Word Problems
Set up the equation total = flat fee + (cost per mile × miles). Subtract the flat fee from the total, then divide by the cost per mile to find the number of miles.
Try a similar one
Concert tickets cost $15 each, plus a $10 booking fee for the whole order. Sam pays $70. How many tickets did Sam buy?
✓ 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
💡 The width, the height and the diagonal make a right triangle, and the diagonal is the hypotenuse. c2 = 122 + 92 = 144 + 81 = 225, so c = √225 = 15. The diagonal is 15 inches long.
✓ Correct!
Not quite. The answer is
💡 The width, the height and the diagonal make a right triangle, and the diagonal is the hypotenuse. c2 = 122 + 92 = 144 + 81 = 225, so c = √225 = 15. The diagonal is 15 inches long.
💡 How to solve: Pythagorean Theorem: Missing Legs & Word Problems
In a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. To find a missing leg, subtract: b2 = c2 - a2, then take the square root. For the diagonal of a box, first find the diagonal of the base, then use it as a leg with the height: d2 = l2 + w2 + h2.
Try a similar one
A right triangle has a leg of 24 and a hypotenuse of 25. Find the other leg.
✓ 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 = 33m + 14. Gym B: y = 17m + 110. Set the costs equal: 33m + 14 = 17m + 110. Subtract 17m from both sides: 16m + 14 = 110. Subtract 14: 16m = 96. Divide by 16: m = 6. Check: Gym A costs 14 + 33 × 6 = 212 and Gym B costs 110 + 17 × 6 = 212. They cost the same after 6 months.
✓ Correct!
Not quite. The answer is
💡 Let m = the number of months and y = the cost in dollars. Gym A: y = 33m + 14. Gym B: y = 17m + 110. Set the costs equal: 33m + 14 = 17m + 110. Subtract 17m from both sides: 16m + 14 = 110. Subtract 14: 16m = 96. Divide by 16: m = 6. Check: Gym A costs 14 + 33 × 6 = 212 and Gym B costs 110 + 17 × 6 = 212. They cost the same after 6 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 school play sold 47 tickets. Adult tickets cost $8 and child tickets cost $6. The play earned $324. 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 t = the number of tickets. The booking fee plus the ticket cost makes what Sam pays: 6 + 12t = 78. Subtract 6 from both sides: 12t = 72. Divide both sides by 12: t = 6. Check: 6 + 12 × 6 = 78. Sam bought 6 tickets.
✓ Correct!
Not quite. The answer is
💡 Let t = the number of tickets. The booking fee plus the ticket cost makes what Sam pays: 6 + 12t = 78. Subtract 6 from both sides: 12t = 72. Divide both sides by 12: t = 6. Check: 6 + 12 × 6 = 78. Sam bought 6 tickets.
💡 How to solve: Word Problems
Set up the equation total = flat fee + (cost per mile × miles). Subtract the flat fee from the total, then divide by the cost per mile to find the number of miles.
Try a similar one
Ana is 11 years older than her brother. The sum of their ages is 29. How old is her brother?
✓ 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
💡 Use a2 + b2 = c2 with the hypotenuse c = 25. b2 = 252 − 72 = 625 − 49 = 576, so b = √576 = 24. The other leg is 24.
✓ Correct!
Not quite. The answer is
💡 Use a2 + b2 = c2 with the hypotenuse c = 25. b2 = 252 − 72 = 625 − 49 = 576, so b = √576 = 24. The other leg is 24.
💡 How to solve: Pythagorean Theorem: Missing Legs & Word Problems
In a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. To find a missing leg, subtract: b2 = c2 - a2, then take the square root. For the diagonal of a box, first find the diagonal of the base, then use it as a leg with the height: d2 = l2 + w2 + h2.
Try a similar one
A right triangle has a leg of 15 and a hypotenuse of 25. Find the other leg.
✓ 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: $4.70 = 470 cents. Let q = quarters and d = dimes. Coins: q + d = 26. Value: 25q + 10d = 470. Multiply the first equation by 10: 10q + 10d = 260. Subtract it from the second: 15q = 210. Divide by 15: q = 14. Then d = 26 − 14 = 12. Check: 25 × 14 + 10 × 12 = 350 + 120 = 470. So Mia has 14 quarters.
✓ Correct!
Not quite. The answer is
💡 Work in cents: $4.70 = 470 cents. Let q = quarters and d = dimes. Coins: q + d = 26. Value: 25q + 10d = 470. Multiply the first equation by 10: 10q + 10d = 260. Subtract it from the second: 15q = 210. Divide by 15: q = 14. Then d = 26 − 14 = 12. Check: 25 × 14 + 10 × 12 = 350 + 120 = 470. So Mia has 14 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
Gym A charges a $10 joining fee plus $38 per month. Gym B charges a $38 joining fee plus $24 per month. After how many months do the two gyms cost the same?
✓ 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 h = the number of hours. The visit charge plus the hourly cost makes the bill: 60 + 30h = 120. Subtract 60 from both sides: 30h = 60. Divide both sides by 30: h = 2. Check: 60 + 30 × 2 = 120. The plumber worked 2 hours.
✓ Correct!
Not quite. The answer is
💡 Let h = the number of hours. The visit charge plus the hourly cost makes the bill: 60 + 30h = 120. Subtract 60 from both sides: 30h = 60. Divide both sides by 30: h = 2. Check: 60 + 30 × 2 = 120. The plumber worked 2 hours.
💡 How to solve: Word Problems
Set up the equation total = flat fee + (cost per mile × miles). Subtract the flat fee from the total, then divide by the cost per mile to find the number of miles.
Try a similar one
Ana is 2 years older than her brother. The sum of their ages is 20. How old is her brother?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Grade 8 Quiz: Word Problems — Easy Version 2
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.