ISEE Middle Level Quiz: Multi Step Word Problems
20 questions · exam conditions
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Multi Step Word ProblemsQuestion 1 of 20

A farmer is building a straight fence that is 120 meters long. He places a fence post at the start of the fence and then a post every 3 meters. If each fence post costs $7, what is the total cost of all the fence posts needed?

$280
$287
$294
$840
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ISEE Middle Level Quiz

ISEE Middle Level Quiz: Multi Step Word Problems

Practice Multi Step Word Problems in ISEE Middle Level with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Multi Step Word Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Middle Level.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A farmer is building a straight fence that is 120 meters long. He places a fence post at the start of the fence and then a post every 3 meters. If each fence post costs $7, what is the total cost of all the fence posts needed?

  1. $280
  2. $287 (correct answer)
  3. $294
  4. $840
Explanation: First, determine the number of 3-meter sections in the fence: 120 meters÷3 meters/section=40120 \text{ meters} \div 3 \text{ meters/section} = 40 sections. For a straight fence with posts at both ends, the number of posts is one more than the number of sections. So, the farmer needs 40+1=4140 + 1 = 41 posts. Finally, calculate the total cost of the posts: 41 \text{ posts} \times \7/\text{post} = $287$.

Question 2

To earn an A in science, Jordan needs an average of at least 92 on five tests. His scores on the first four tests are 88, 95, 86, and 94. What is the minimum score Jordan must get on the fifth test to earn an A?

  1. 92
  2. 95
  3. 97 (correct answer)
  4. 98
Explanation: First, find the total score Jordan needs across all five tests to have an average of 92. This is 5×92=4605 \times 92 = 460. Next, find the sum of his scores on the first four tests: 88+95+86+94=36388 + 95 + 86 + 94 = 363. Finally, subtract the sum of the first four scores from the target total score to find the required score on the fifth test: 460−363=97460 - 363 = 97.

Question 3

A charity fundraiser receives donations from 120 people. The average donation is $25. A local company agrees to match every dollar donated above a total of $2,000. How much money will the company donate?

  1. $1,000 (correct answer)
  2. $2,000
  3. $3,000
  4. $5,000
Explanation: First, calculate the total amount of money donated by the people: 120 \text{ people} \times \25/\text{person} = $3,000.Thecompanymatchestheamountdonatedabove$2,000.Tofindthisamount,subtractthethresholdfromthetotaldonations:. The company matches the amount donated above $2,000. To find this amount, subtract the threshold from the total donations: $3,000 - $2,000 = $1,000$. The company will donate this matched amount, which is $1,000.

Question 4

A bag of 96 candies is to be shared among three friends: Amy, Beth, and Carla. Amy gets 14\frac{1}{4} of the candies. Beth gets 13\frac{1}{3} of the remaining candies. Carla gets the rest. How many more candies does Carla get than Amy?

  1. 16
  2. 24 (correct answer)
  3. 32
  4. 48
Explanation: First, find how many candies Amy gets: 96×14=2496 \times \frac{1}{4} = 24 candies. Next, find the number of remaining candies: 96−24=7296 - 24 = 72 candies. Then, find how many candies Beth gets from the remainder: 72×13=2472 \times \frac{1}{3} = 24 candies. Carla gets the rest, which is 72−24=4872 - 24 = 48 candies. Finally, find the difference between Carla's and Amy's shares: 48−24=2448 - 24 = 24 candies.

Question 5

An employee earns $15 per hour for the first 40 hours worked in a week. For any hours worked over 40, the employee earns 1.5 times the regular hourly rate. If the employee worked 46 hours in one week, what were their total earnings for that week?

  1. $690.00
  2. $699.00
  3. $735.00 (correct answer)
  4. $1,035.00
Explanation: First, calculate the earnings for the first 40 hours: 40 \text{ hours} \times \15/\text{hour} = $600.Next,determinethenumberofovertimehours:. Next, determine the number of overtime hours: 46 - 40 = 6hours.Then,calculatetheovertimerate:hours. Then, calculate the overtime rate:$15 \times 1.5 = $22.50perhour.Calculatetheovertimeearnings:per hour. Calculate the overtime earnings:6 \text{ hours} \times $22.50/\text{hour} = $135.Finally,addtheregularearningsandovertimeearnings:. Finally, add the regular earnings and overtime earnings: $600 + $135 = $735.00$.

Question 6

A recipe for a batch of cookies requires 34\frac{3}{4} cup of sugar. Liam wants to make 3 batches of cookies. He starts with a bag containing 4 cups of sugar. After making the cookies, how much sugar is left in the bag?

  1. 1141 \frac{1}{4} cups
  2. 1341 \frac{3}{4} cups (correct answer)
  3. 2142 \frac{1}{4} cups
  4. 3143 \frac{1}{4} cups
Explanation: First, calculate the total amount of sugar needed for 3 batches. This is 3×34=943 \times \frac{3}{4} = \frac{9}{4} cups. Convert the improper fraction to a mixed number: 94=214\frac{9}{4} = 2 \frac{1}{4} cups. Then, subtract the amount of sugar used from the initial amount: 4−214=1344 - 2 \frac{1}{4} = 1 \frac{3}{4} cups.

Question 7

Maya withdrew some money from her bank account. She spent $35 on a shirt. Then she gave half of the remaining money to her brother. If she has $40 left, how much money did she withdraw from her account originally?

  1. $75
  2. $90
  3. $115 (correct answer)
  4. $150
Explanation: This problem is best solved by working backward. Maya has $40 left after giving half of her money to her brother. So, before giving him money, she had \40 \times 2 = $80.Beforethat,shespent$35onashirt.Tofindtheamountshehadbeforethepurchase,addthatamountback:. Before that, she spent $35 on a shirt. To find the amount she had before the purchase, add that amount back: $80 + $35 = $115$. This was the amount she originally withdrew.

Question 8

A printer can print 240 pages in 8 minutes. The printer jams and is stopped for 5 minutes. After the jam is cleared, it prints another 300 pages at the same rate. What is the total time, in minutes, from the start of printing to the end?

  1. 18
  2. 21
  3. 23 (correct answer)
  4. 26
Explanation: First, find the printing rate: 240 pages÷8 minutes=30240 \text{ pages} \div 8 \text{ minutes} = 30 pages per minute. Next, find the time it takes to print the second batch of 300 pages: 300 pages÷30 pages/minute=10300 \text{ pages} \div 30 \text{ pages/minute} = 10 minutes. Finally, add all the time segments together: 8 minutes+5 minutes+10 minutes=238 \text{ minutes} + 5 \text{ minutes} + 10 \text{ minutes} = 23 minutes.

Question 9

A factory produces 1,500 toy cars in a shift. The cars are packed into boxes that hold 24 cars each. The filled boxes are then packed into crates that hold 10 boxes each. How many toy cars are left over that do not make up a full crate?

  1. 12
  2. 48
  3. 60 (correct answer)
  4. 240
Explanation: First, find the number of full boxes that can be packed: 1,500÷24=62.51,500 \div 24 = 62.5. This means 62 full boxes and 0.5×24=120.5 \times 24 = 12 leftover cars. Next, find how many full crates can be made from the 62 boxes: 62÷10=6.262 \div 10 = 6.2. This means 6 full crates and 2 leftover boxes. The cars left over that do not make up a full crate are the cars in the 2 leftover boxes plus the 12 loose cars. The number of cars is (2 boxes×24 cars/box)+12 cars=48+12=60(2 \text{ boxes} \times 24 \text{ cars/box}) + 12 \text{ cars} = 48 + 12 = 60 cars.

Question 10

A library charges a fine of $0.25 per day for an overdue book. For a book that is more than 10 days overdue, there is an additional flat fee of $5.00. If a book is returned 18 days overdue, what is the total fine?

  1. $4.50
  2. $7.00
  3. $9.50 (correct answer)
  4. $10.00
Explanation: First, calculate the daily fine for the entire overdue period: 18 \text{ days} \times \0.25/\text{day} = $4.50.Sincethebookis18daysoverdue,whichismorethan10days,theadditional$5.00flatfeeapplies.Addthedailyfineandtheflatfeetofindthetotalfine:. Since the book is 18 days overdue, which is more than 10 days, the additional $5.00 flat fee applies. Add the daily fine and the flat fee to find the total fine: $4.50 + $5.00 = $9.50$.

Question 11

A rectangular garden is 12 feet long and 8 feet wide. The owner wants to cover the garden with topsoil that costs $3 per square foot. The owner has a budget of $300 for the topsoil. How much money will be left after buying the topsoil?

  1. $12 (correct answer)
  2. $24
  3. $204
  4. $288
Explanation: First, calculate the area of the garden: Area=length×width=12 ft×8 ft=96 sq ftArea = length \times width = 12 \text{ ft} \times 8 \text{ ft} = 96 \text{ sq ft}. Next, calculate the total cost of the topsoil: 96 \text{ sq ft} \times \3/\text{sq ft} = $288.Finally,subtractthecostfromthebudgettofindtheremainingmoney:. Finally, subtract the cost from the budget to find the remaining money: $300 - $288 = $12$.

Question 12

An athlete runs for 20 minutes and burns 12 calories per minute. She then lifts weights for half an hour, burning an additional 150 calories. Finally, she swims for a quarter of an hour, burning another 100 calories. How many total calories did she burn during this workout?

  1. 240
  2. 390
  3. 490 (correct answer)
  4. 510
Explanation: First, calculate the calories burned from running: 20 minutes×12 calories/minute=24020 \text{ minutes} \times 12 \text{ calories/minute} = 240 calories. The calories burned from weightlifting (150) and swimming (100) are given directly. To find the total calories burned, add the calories from all three activities: 240+150+100=490240 + 150 + 100 = 490 calories. The time spent on weightlifting and swimming are extra information.

Question 13

A fish tank in the shape of a rectangular prism is 50 cm long, 30 cm wide, and 40 cm high. It is filled with water to a height of 35 cm. If 1 liter is equal to 1,000 cubic centimeters, how many liters of water are in the tank?

  1. 52.5 (correct answer)
  2. 60
  3. 5,250
  4. 52,500
Explanation: First, calculate the volume of the water in the tank, using the height of the water (35 cm), not the height of the tank. Volume = length × width × height of water = 50 cm×30 cm×35 cm=52,500 cm350 \text{ cm} \times 30 \text{ cm} \times 35 \text{ cm} = 52,500 \text{ cm}^3. Next, convert the volume from cubic centimeters to liters using the given conversion: 52,500 cm3÷1,000 cm3/L=52.5 L52,500 \text{ cm}^3 \div 1,000 \text{ cm}^3/\text{L} = 52.5 \text{ L}.

Question 14

The temperature in a town was -8°F at 6:00 AM. The temperature rose by 3°F each hour for the next 5 hours. Then, it dropped by 12°F over the next 6 hours. What was the temperature at 5:00 PM?

  1. -5°F (correct answer)
  2. 3°F
  3. 7°F
  4. 11°F
Explanation: First, calculate the total temperature increase over the first 5 hours: 5 hours×3°F/hour=15°F5 \text{ hours} \times 3°F/\text{hour} = 15°F. Then, calculate the temperature at 11:00 AM (5 hours after 6:00 AM): −8°F+15°F=7°F-8°F + 15°F = 7°F. Finally, calculate the temperature at 5:00 PM (6 hours later) after it dropped by 12°F: 7°F−12°F=−5°F7°F - 12°F = -5°F.

Question 15

At a carnival, Ben won 12 tickets. Sarah won twice as many tickets as Ben. Marco won 8 fewer tickets than Sarah. How many tickets did they win in total?

  1. 36
  2. 40
  3. 52 (correct answer)
  4. 60
Explanation: First, find the number of tickets Sarah won: 12×2=2412 \times 2 = 24 tickets. Next, find the number of tickets Marco won: 24−8=1624 - 8 = 16 tickets. Finally, add the number of tickets each person won to find the total: 12 (Ben)+24 (Sarah)+16 (Marco)=5212 \text{ (Ben)} + 24 \text{ (Sarah)} + 16 \text{ (Marco)} = 52 tickets.

Question 16

A school is planning a field trip for 130 students and 12 adults. Each bus can hold a maximum of 48 people. What is the total number of empty seats on all the buses used for the trip?

  1. 2 (correct answer)
  2. 14
  3. 46
  4. 50
Explanation: First, find the total number of people going on the trip: 130+12=142130 + 12 = 142 people. Next, determine the minimum number of buses needed by dividing the total people by the bus capacity: 142÷48=2142 \div 48 = 2 with a remainder of 46. Since there is a remainder, 3 buses are needed. Then, calculate the total number of seats on 3 buses: 3×48=1443 \times 48 = 144 seats. Finally, subtract the number of people from the total number of seats to find the number of empty seats: 144−142=2144 - 142 = 2.

Question 17

A recipe for 6 servings uses 1.50 cups rice and 3.00 cups broth; what are the adjusted ingredient amounts for 15 servings?

  1. Use 3.75 cups rice and 7.50 cups broth (correct answer)
  2. Use 2.50 cups rice and 5.00 cups broth
  3. Use 4.50 cups rice and 9.00 cups broth
  4. Use 1.50 cups rice and 3.00 cups broth
Explanation: This question tests ISEE Middle Level quantitative reasoning skills, specifically solving multi-step word problems using the four operations. Multi-step problems require students to apply the correct sequence of operations to reach a logical solution, often requiring addition, subtraction, multiplication, and division. In this problem, students must scale a recipe from 6 to 15 servings, executing calculations in the correct order. The correct answer is achieved by finding the scaling factor (15 ÷ 6 = 2.5), then multiplying each ingredient: rice (1.50 × 2.5 = 3.75 cups) and broth (3.00 × 2.5 = 7.50 cups). A common distractor might involve using an incorrect scaling factor or only scaling one ingredient. To help students: Teach them to always find the ratio of new servings to original servings first, then apply this factor consistently to all ingredients.

Question 18

A school bake sale sells brownies for $1.50 each and cookies for $0.75 each. The ingredients cost a total of $45. If they sell 60 brownies and 80 cookies, what is the total profit from the bake sale?

  1. $90
  2. $105 (correct answer)
  3. $150
  4. $195
Explanation: First, calculate the total revenue from selling brownies: 60 \times \1.50 = $90.Next,calculatethetotalrevenuefromsellingcookies:. Next, calculate the total revenue from selling cookies: 80 \times $0.75 = $60.Then,findthetotalrevenue:. Then, find the total revenue: $90 + $60 = $150.Finally,calculatetheprofitbysubtractingthecostofingredientsfromthetotalrevenue:. Finally, calculate the profit by subtracting the cost of ingredients from the total revenue: Profit = Revenue - Cost = $150 - $45 = $105$.

Question 19

You have a $250.00 event budget; you pay $85.00 for a venue, $9.50 per person for 12 guests, and $30.00 for music. What is the final budget after all expenses?

  1. The final budget is $21.00 (correct answer)
  2. The final budget is $135.00
  3. The final budget is $5.00
  4. The final budget is $151.00
Explanation: This question tests ISEE Middle Level quantitative reasoning skills, specifically solving multi-step word problems using the four operations. Multi-step problems require students to apply the correct sequence of operations to reach a logical solution, often requiring addition, subtraction, multiplication, and division. In this problem, students must interpret an event budget scenario with multiple expenses, executing calculations in the correct order. The correct answer is achieved by calculating total expenses: venue (85.00)+catering(85.00) + catering (9.50 × 12 = 114.00)+music(114.00) + music (30.00) = 229.00,thensubtractingfromthebudget(229.00, then subtracting from the budget (250.00 - $229.00 = $21.00). A common distractor might involve forgetting to multiply the per-person cost by the number of guests or adding instead of subtracting expenses. To help students: Teach them to list all expenses separately, perform any multiplication first, then sum all costs before subtracting from the total budget.

Question 20

A road trip has legs of 120 miles, 85 miles, and 95 miles; at 25 miles per gallon, how much fuel is needed for the entire trip?

  1. The fuel needed is 12.00 gallons (correct answer)
  2. The fuel needed is 10.00 gallons
  3. The fuel needed is 7.50 gallons
  4. The fuel needed is 300.00 gallons
Explanation: This question tests ISEE Middle Level quantitative reasoning skills, specifically solving multi-step word problems using the four operations. Multi-step problems require students to apply the correct sequence of operations to reach a logical solution, often requiring addition, subtraction, multiplication, and division. In this problem, students must interpret a road trip scenario with multiple legs and fuel efficiency, executing calculations in the correct order. The correct answer is achieved by first finding the total distance (120 + 85 + 95 = 300 miles), then dividing by the fuel efficiency (300 ÷ 25 = 12 gallons). A common distractor might involve dividing individual legs by the fuel efficiency separately or confusing miles with gallons. To help students: Teach them to identify what the question asks for (total fuel), combine all distances first, then apply the fuel efficiency calculation as a final step.