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Grade 9 Quiz: Word Problems — Easy Version 2
Grade 9 · Whoobee 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: A rental shop has bicycles (x) and tricycles (y). There are 12 of them with 28 wheels in total. How many bicycles and tricycles are there?
Answer: x = 8, y = 4
Not quite. The answer is
💡 Omar does 14 of the job each hour and Lily does 112. Together they do 14 + 112 = 312 + 112 = 412 = 13 of the job per hour. Time for the whole job = 1 ÷ rate = 1 ÷ 13 = 3 hours.
✓ Correct!
Not quite. The answer is
💡 Omar does 14 of the job each hour and Lily does 112. Together they do 14 + 112 = 312 + 112 = 412 = 13 of the job per hour. Time for the whole job = 1 ÷ rate = 1 ÷ 13 = 3 hours.
💡 How to solve: Mixture & Work Word Problems
Mixture: (amount × strength) of each part adds up to (total amount × strength of the mixture). Call the unknown amount x and solve, for example 0.20x + 0.50(10) = 0.40(x + 10). Prices work the same way with cost per pound in place of percent. Work: someone who needs a hours does 1a of the job each hour. Add the rates: 1a + 1b = 1t, so together they need t = a × ba + b hours.
Try a similar one
How many liters of pure alcohol are in 80 liters of a 45% alcohol solution?
✓ 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
💡 Mia is older by 26, so x − y = 26. Their ages add up to 54, so x + y = 54. Add the two equations (the y's cancel): 2x = 54 + 26 = 80, so x = 80 ÷ 2 = 40. Put x = 40 into x + y = 54: y = 54 − 40 = 14. So x = 40, y = 14.
✓ Correct!
Not quite. The answer is
💡 Mia is older by 26, so x − y = 26. Their ages add up to 54, so x + y = 54. Add the two equations (the y's cancel): 2x = 54 + 26 = 80, so x = 80 ÷ 2 = 40. Put x = 40 into x + y = 54: y = 54 − 40 = 14. So x = 40, y = 14.
💡 How to solve: Word Problems
Let the two numbers be x and y and write x + y = sum and x − y = difference. Add the equations to get 2x = sum + difference, so x = (sum + difference) ÷ 2, then y = sum − x. Write the answer as x = a, y = b.
Try a similar one
A rental shop has bicycles (x) and tricycles (y). There are 15 of them with 36 wheels in total. How many bicycles and tricycles are there?
✓ 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
💡 Ivan does 17 of the job each hour. Work = rate × time = 17 × 4 = 47. So Ivan finishes 47 of the job.
✓ Correct!
Not quite. The answer is
💡 Ivan does 17 of the job each hour. Work = rate × time = 17 × 4 = 47. So Ivan finishes 47 of the job.
💡 How to solve: Mixture & Work Word Problems
Mixture: (amount × strength) of each part adds up to (total amount × strength of the mixture). Call the unknown amount x and solve, for example 0.20x + 0.50(10) = 0.40(x + 10). Prices work the same way with cost per pound in place of percent. Work: someone who needs a hours does 1a of the job each hour. Add the rates: 1a + 1b = 1t, so together they need t = a × ba + b hours.
Try a similar one
How many liters of pure salt are in 80 liters of a 25% salt solution?
✓ 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 sum gives x + y = 18 and the difference gives x − y = 2. Add the two equations (the y's cancel): 2x = 18 + 2 = 20, so x = 20 ÷ 2 = 10. Put x = 10 into x + y = 18: y = 18 − 10 = 8. So x = 10, y = 8.
✓ Correct!
Not quite. The answer is
💡 The sum gives x + y = 18 and the difference gives x − y = 2. Add the two equations (the y's cancel): 2x = 18 + 2 = 20, so x = 20 ÷ 2 = 10. Put x = 10 into x + y = 18: y = 18 − 10 = 8. So x = 10, y = 8.
💡 How to solve: Word Problems
Let the two numbers be x and y and write x + y = sum and x − y = difference. Add the equations to get 2x = sum + difference, so x = (sum + difference) ÷ 2, then y = sum − x. Write the answer as x = a, y = b.
Try a similar one
A test has 13 questions worth 32 points in all. Some are worth 2 points (x) and the rest 5 points (y). How many of each kind are there?
✓ 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
💡 Pounds × price per pound gives the cost of each part, and the parts add up to the cost of the mixture. 1(3) + 1(7) = 2c, where c is the mixture's value. So 3 + 7 = 2c and 10 = 2c. Divide both sides by 2: c = 10 ÷ 2 = 5. The mixture costs $5 per pound.
✓ Correct!
Not quite. The answer is
💡 Pounds × price per pound gives the cost of each part, and the parts add up to the cost of the mixture. 1(3) + 1(7) = 2c, where c is the mixture's value. So 3 + 7 = 2c and 10 = 2c. Divide both sides by 2: c = 10 ÷ 2 = 5. The mixture costs $5 per pound.
💡 How to solve: Mixture & Work Word Problems
Mixture: (amount × strength) of each part adds up to (total amount × strength of the mixture). Call the unknown amount x and solve, for example 0.20x + 0.50(10) = 0.40(x + 10). Prices work the same way with cost per pound in place of percent. Work: someone who needs a hours does 1a of the job each hour. Add the rates: 1a + 1b = 1t, so together they need t = a × ba + b hours.
Try a similar one
How many liters of pure sugar are in 40 liters of a 5% sugar solution?
✓ 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 = 2-point questions and y = 5-point questions. Questions: x + y = 6. Points: 2x + 5y = 18. Multiply the first equation by 2: 2x + 2y = 12. Subtract it from the second: 3y = 18 − 12 = 6, so y = 6 ÷ 3 = 2. Then x = 6 − 2 = 4. So x = 4, y = 2.
✓ Correct!
Not quite. The answer is
💡 Let x = 2-point questions and y = 5-point questions. Questions: x + y = 6. Points: 2x + 5y = 18. Multiply the first equation by 2: 2x + 2y = 12. Subtract it from the second: 3y = 18 − 12 = 6, so y = 6 ÷ 3 = 2. Then x = 6 − 2 = 4. So x = 4, y = 2.
💡 How to solve: Word Problems
Let the two numbers be x and y and write x + y = sum and x − y = difference. Add the equations to get 2x = sum + difference, so x = (sum + difference) ÷ 2, then y = sum − x. Write the answer as x = a, y = b.
Try a similar one
Sandwiches (x) cost $4 and drinks (y) cost $2. A group buys 11 items for $36. How many sandwiches and drinks did they 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
💡 Pure alcohol = amount × concentration = 40 × 20% = 40 × 20 ÷ 100 = 800 ÷ 100 = 8. There are 8 liters of pure alcohol.
✓ Correct!
Not quite. The answer is
💡 Pure alcohol = amount × concentration = 40 × 20% = 40 × 20 ÷ 100 = 800 ÷ 100 = 8. There are 8 liters of pure alcohol.
💡 How to solve: Mixture & Work Word Problems
Mixture: (amount × strength) of each part adds up to (total amount × strength of the mixture). Call the unknown amount x and solve, for example 0.20x + 0.50(10) = 0.40(x + 10). Prices work the same way with cost per pound in place of percent. Work: someone who needs a hours does 1a of the job each hour. Add the rates: 1a + 1b = 1t, so together they need t = a × ba + b hours.
Try a similar one
How many liters of pure acid are in 20 liters of a 10% acid solution?
✓ 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 = bicycles and y = tricycles. Vehicles: x + y = 18. Wheels: 2x + 3y = 42. Multiply the first equation by 2: 2x + 2y = 36. Subtract it from the second: y = 42 − 36 = 6. Then x = 18 − 6 = 12. So x = 12, y = 6.
✓ Correct!
Not quite. The answer is
💡 Let x = bicycles and y = tricycles. Vehicles: x + y = 18. Wheels: 2x + 3y = 42. Multiply the first equation by 2: 2x + 2y = 36. Subtract it from the second: y = 42 − 36 = 6. Then x = 18 − 6 = 12. So x = 12, y = 6.
💡 How to solve: Word Problems
Let the two numbers be x and y and write x + y = sum and x − y = difference. Add the equations to get 2x = sum + difference, so x = (sum + difference) ÷ 2, then y = sum − x. Write the answer as x = a, y = b.
Try a similar one
A test has 17 questions worth 70 points in all. Some are worth 2 points (x) and the rest 5 points (y). How many of each kind are there?
✓ 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
💡 Amount × concentration gives the acid in each part, and the parts add up to the mixture. 4(10) + 1(60) = 5c, where c is the mixture's value. So 40 + 60 = 5c and 100 = 5c. Divide both sides by 5: c = 100 ÷ 5 = 20. The mixture is 20% acid.
✓ Correct!
Not quite. The answer is
💡 Amount × concentration gives the acid in each part, and the parts add up to the mixture. 4(10) + 1(60) = 5c, where c is the mixture's value. So 40 + 60 = 5c and 100 = 5c. Divide both sides by 5: c = 100 ÷ 5 = 20. The mixture is 20% acid.
💡 How to solve: Mixture & Work Word Problems
Mixture: (amount × strength) of each part adds up to (total amount × strength of the mixture). Call the unknown amount x and solve, for example 0.20x + 0.50(10) = 0.40(x + 10). Prices work the same way with cost per pound in place of percent. Work: someone who needs a hours does 1a of the job each hour. Add the rates: 1a + 1b = 1t, so together they need t = a × ba + b hours.
Try a similar one
How many liters of pure acid are in 60 liters of a 10% acid solution?
✓ 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 = quarters and y = dimes. Coins: x + y = 18. Value in cents: 25x + 10y = 390. Multiply the first equation by 10: 10x + 10y = 180. Subtract it from the second: 15x = 390 − 180 = 210, so x = 210 ÷ 15 = 14. Then y = 18 − 14 = 4. So x = 14, y = 4.
✓ Correct!
Not quite. The answer is
💡 Let x = quarters and y = dimes. Coins: x + y = 18. Value in cents: 25x + 10y = 390. Multiply the first equation by 10: 10x + 10y = 180. Subtract it from the second: 15x = 390 − 180 = 210, so x = 210 ÷ 15 = 14. Then y = 18 − 14 = 4. So x = 14, y = 4.
💡 How to solve: Word Problems
Let the two numbers be x and y and write x + y = sum and x − y = difference. Add the equations to get 2x = sum + difference, so x = (sum + difference) ÷ 2, then y = sum − x. Write the answer as x = a, y = b.
Try a similar one
Mia (x) is 14 years older than her cousin Leo (y). Together their ages add up to 26. How old is each?
✓ 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 9 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.