Math Word Problems quiz

Multi-Step Word Problems Quiz

Practice 10 multi-step word problems that combine quantities, constraints, equations, percentages, rates, geometry, averages, and intermediate results. Use hints when needed and review the explanation after each answer.

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1 Question 1 of 10

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A family has a monthly take-home income of $4,200. They spend 32% on housing, $680 on food, $420 on transportation, and $260 on utilities. They want to save 15% of their income. How much money remains after all expenses and savings?

Hint: Find the housing cost and savings first, then subtract all expenses and savings from the income.

Explanation: Housing = 0.32 × 4,200 = $1,344. Savings = 0.15 × 4,200 = $630. Other expenses total $680 + $420 + $260 = $1,360. Total outflow = 1,344 + 630 + 1,360 = $3,334. Remaining money = 4,200 - 3,334 = $866.

2 Question 2 of 10

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A delivery driver travels 126 miles at 63 mph, takes a 30-minute break, then drives 84 miles at 56 mph. What is the driver's average speed for the entire trip, including the break?

Hint: Find the time for each driving segment, include the 0.5-hour break, then divide total distance by total elapsed time.

Explanation: First leg time = 126 ÷ 63 = 2 hours. Second leg time = 84 ÷ 56 = 1.5 hours. Including the 0.5-hour break, total time = 4 hours. Total distance = 210 miles. Average speed = 210 ÷ 4 = 52.5 mph.

3 Question 3 of 10

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A rectangular patio is 12 meters by 8 meters. Paving stones cost $18 per square meter, and 7% extra material is ordered for cutting and waste. What is the total cost of the paving stones?

Hint: Find the patio area, increase it by 7%, then multiply by the cost per square meter.

Explanation: Patio area = 12 × 8 = 96 m². With 7% extra, material needed = 96 × 1.07 = 102.72 m². Cost = 102.72 × $18 = $1,848.96.

4 Question 4 of 10

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A juice mixture contains orange juice and water in a 3:2 ratio. There are 25 liters of mixture. Then 5 liters of water are added. What percent of the new mixture is orange juice?

Hint: Find the original amount of orange juice from the 3:2 ratio, then divide by the new total volume.

Explanation: The original 25 liters contain 5 ratio parts, so each part is 5 liters. Orange juice = 3 × 5 = 15 liters. After adding 5 liters of water, total volume = 30 liters. Orange percentage = 15 ÷ 30 = 50%.

5 Question 5 of 10

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A student has test scores of 78, 84, 91, and 87. A fifth test counts twice as much as each of the first four tests. What score must the student earn on the fifth test to have a weighted average of 88?

Hint: The total weight is 6. Set up a weighted-average equation with the fifth score counted twice.

Explanation: The first four scores sum to 340. Let the fifth score be x and count it twice. For a weighted average of 88 over total weight 6: (340 + 2x) ÷ 6 = 88. So 340 + 2x = 528, giving 2x = 188 and x = 94.

6 Question 6 of 10

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Four identical machines produce 1,440 parts in 6 hours. After 2 hours, one machine stops working. If the remaining three machines continue at the same individual rate, how many parts are produced in the full 6-hour period?

Hint: Find the production rate of one machine per hour. Then calculate the first 2 hours with four machines and the last 4 hours with three machines.

Explanation: One machine produces 1,440 ÷ (4 × 6) = 60 parts per hour. First 2 hours: 4 × 2 × 60 = 480 parts. Last 4 hours: 3 × 4 × 60 = 720 parts. Total = 480 + 720 = 1,200 parts.

7 Question 7 of 10

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A $240 jacket is discounted by 25%. A coupon then takes an additional 10% off the discounted price, and 8% sales tax is applied after both discounts. What is the final price?

Hint: Apply the 25% discount, then the additional 10% discount, then the 8% tax in that order.

Explanation: After 25% off: $240 × 0.75 = $180. After another 10% off: $180 × 0.90 = $162. After 8% tax: $162 × 1.08 = $174.96.

8 Question 8 of 10

Not answered

Adult tickets to a school play cost $14 and student tickets cost $9. A total of 120 tickets are sold for $1,365. How many adult tickets were sold?

Hint: Let a be adult tickets and use student tickets = 120 - a. Build a revenue equation.

Explanation: Let a be the number of adult tickets. Then student tickets = 120 - a. Revenue equation: 14a + 9(120 - a) = 1,365. This gives 14a + 1,080 - 9a = 1,365, so 5a = 285 and a = 57.

9 Question 9 of 10

Not answered

A water tank is 2.5 meters long, 1.8 meters wide, and 1.2 meters high. It is currently 40% full. Water enters at 90 liters per minute for 20 minutes. What percent full is the tank after the 20 minutes? Use 1 m³ = 1,000 liters.

Hint: Find the tank capacity in liters, then the initial water volume, then add the incoming water.

Explanation: Tank capacity = 2.5 × 1.8 × 1.2 = 5.4 m³ = 5,400 liters. Initially it contains 0.40 × 5,400 = 2,160 liters. Added water = 90 × 20 = 1,800 liters. New volume = 3,960 liters. Percent full = 3,960 ÷ 5,400 ≈ 0.7333 = 73.3%.

10 Question 10 of 10

Not answered

A store buys 80 lamps for $22 each. It sells 60 lamps at $35 each and the remaining 20 lamps at a 20% discount from the $35 selling price. What is the store's total profit?

Hint: Find the total cost, the revenue from the first 60 lamps, and the discounted selling price for the last 20 lamps.

Explanation: Total cost = 80 × $22 = $1,760. Revenue from 60 lamps = 60 × $35 = $2,100. Discounted price = $35 × 0.80 = $28, so revenue from 20 lamps = 20 × $28 = $560. Total revenue = $2,660. Profit = $2,660 - $1,760 = $900.

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Problem-solving workshop

Multi-step problems are chains: each result becomes information for the next decision

These 10 questions combine percentages, rates, geometry, budgets, weighted averages, production, discounts, equations, capacity, and profit. The challenge is not any single operation; it is keeping track of what each intermediate result means and whether it should be reused, added, subtracted, or converted.

PercentagesRatesGeometryBudgets Weighted averagesProductionEquationsCapacity

Five-step solving chain

A reliable multi-step solution has visible checkpoints

Use this sequence whenever a problem mixes several operations or constraints.

1IdentifyWhat is known?

2ModelWhich relationship?

3ComputeFind an intermediate result

4ReuseFeed it into the next step

5CheckUnits and reasonableness

Budget cascade

Some problems require several categories to be computed before the final subtraction

Monthly income: $4,200

Housing: 32%$1,344

Other fixed expenses$1,360

Savings: 15%$630

Final balance

Total outflow = $1,344 + $1,360 + $630 = $3,334.

$4,200 − $3,334 = $866 remaining.

Intermediate-result relay

One answer becomes the next input

12 × 8 = 96 m²

96 × 1.07 = 102.72 m²

102.72 × $18 = $1,848.96

The patio problem cannot be solved correctly by applying 7% directly to the price or by multiplying $18 by the original area and stopping.

Area → waste allowance → material quantity → cost.

Model selector

Different multi-step problems fail for different reasons

Before calculating, identify the dominant mathematical structure.

Successive percentagesdiscounts, tax, savings, growth

Rates over timetravel, production, filling

Equation constraintstickets, weighted averages, unknown quantities

Measurementarea, volume, units, capacity

Constraint board

When two conditions must both be satisfied, build an equation before guessing

Ticket problem

120 total tickets, adults at $14, students at $9, total revenue $1,365.

14a + 9(120 − a) = 1365

Weighted-average problem

The fifth test counts twice, so its weight must appear twice in the total.

(340 + 2x) / 6 = 88

Capacity chain

Unit conversion can be a middle step rather than the end of the problem

Capacity: 2.5 × 1.8 × 1.2 = 5.4 m³

Convert: 5.4 m³ = 5,400 L

Initial water: 40% = 2,160 L

Add: 90 × 20 = 1,800 L

New fill: 3,960 / 5,400 = 73.3%

After the quiz

Review the step where the chain broke

In multi-step problems, the final arithmetic may be correct even when an earlier intermediate value is wrong.

PlanningDid you choose the right sequence of operations?

Intermediate valuesDid each result keep the correct meaning and unit?

ConstraintsDid the equation represent every condition?

Final checkDoes the result fit the context and expected size?

Math Word Problems Percentage Word Problems