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Middle School Archive

Browse Middle School Word Problems
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Selected answers to common questions:
    Mixture problems.

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Shadow Game [01/28/2001]

Tom is 6 feet tall and Carol is 5 feet tall. If Carol stands at the "shadow top" of Tom's head, their two combined shadows total 15 feet. How long is each shadow?

Sharing Money [01/25/1997]

Three people have various numbers of coins. How can they share the coins so that each has the same amount of money?

Sharing the Cost of the Weekend Trip [07/24/2003]

A group of people planned to rent a large beach house for a weekend trip. They were to share the $800 cost equally. However, two people were unable to go and this increased the cost for each person by $20. How many persons were in the original group?

Sheep Shearing Rule [03/20/2003]

Eric the sheep is waiting in line to be shorn. Each time a sheep at the front of the line gets shorn, Eric sneaks up line four places. Describe a rule you could use to find the number of sheep shorn before Eric for any number of sheep in front of him.

Shopping [8/26/1996]

Which items should a shopper buy if she wants to spend as much of the $62.00 she has as possible?

Simple Equations from Word Problems [5/23/1996]

I'm having trouble with some problem-solving questions...

Simultaneous Equations [08/10/1997]

A, B, and C can finish a job in 6 days... In how many days can each man working alone do the job?

Single Variable Algebraic Mixture Problem [05/03/2005]

Brittany needs a mixture of 76% oats and 24% corn. She currently has 25 pounds of a mixture that is 28% oats. How many pounds of oats should be added to the mixture?

Six Chickens, Five Minutes [01/09/2003]

If 1 and 1/2 chickens lay 1 and 1/2 eggs in 1 and 1/2 minutes, how many eggs will 6 chickens lay in 5 minutes?

Six Quarts of Water, 2 Containers [08/24/1997]

How can you measure 6 quarts of water with only 4-qt. and 9-qt. pails?

Snails Crossing the Lawn [07/26/1997]

It takes 10 snails 50 minutes to cross a lawn from when the first snail slithers on to the lawn to the moment the last snail leaves...

Solution Using Verbal Argument and Model [02/06/2002]

Mr. Li has fewer than 200 sweets. He wants to give each pupil in his class an equal number of sweets. If he gives each pupil 2 sweets, he will have 70 sweets left over; if 4, he will need 10 more sweets. How many pupils are there in the class? How many sweets does Mr. Li have?

Solve a Simpler Problem [09/25/2000]

What day of the week is the 3,824th day after Wednesday? How will this help me in life?

Solving a Fraction Problem Using Common Sense [03/21/2004]

When the gun sounded, only two-fifths of the racers began to run. If 460 racers began to run, how many racers were there in all? Can you show me how to figure out what a fraction is without knowing the total number?

Solving a Math Poem [05/24/2000]

Take five times which plus half of what, and make the square of what you've got...

Solving a Mixture Problem Intuitively and with Algebra [07/06/2007]

There are 7 litres of turpentine in a mixture of 21 litres of water and turpentine. How many litres of turpentine must be added to make a mixture of 75% turpentine?

Solving an Algebra Word Problem [10/11/1995]

Two members of the track team spent 18 h in total training one week. Amy spent 2h 20 min more than Becky. How long did each spend?

Solving a Typical Rate-Time-Distance Problem [09/02/2005]

A look at how to use algebra to solve problems involving rates, times, and distances. The problem in this example centers around walking and running at two different rates for a total of 3 hours.

Solving for Multiple Unknowns [03/22/2003]

Three chickens and one duck cost as much as two geese. One chicken, two ducks and three geese cost $25. What is the cost of each bird?

Solving for Time [2/1/1996]

You are traveling 55 mph over a bridge that is 4260 ft. long. How long does it take to cross the bridge?

Solving Multi-Step Problems [11/01/2003]

Mary and Patty leave their house at 2 o'clock, following the same route. Patty walks at a steady pace of 4 mph. Mary walks at a leisurely rate of 2 mph for 2 hours and then jogs at 6 mph. When will Mary catch up with Patty?

Solving Problems Involving Rate, Time, and Distance [09/12/2004]

George lives approximately 15 miles from work. He is currently driving 35 mph. Assuming that his speed will remain constant, how long will it take George to reach work?

Speed of Two Trains [7/31/1996]

A train leaves Chicago for Indianapolis, 216 km away, at 9 a.m. One hour later, a train leaves Indianapolis for Chicago.... find the speed of each train.

Splitting Peanuts [08/03/2002]

On a camping trip, the family had brought many bags of peanuts for snacks...

Square Dance Partners, Trip Budget [6/30/1996]

1) Sally invited 17 guests to her party...Everyone had to have a partner so that the sum of each couple's number was a perfect square... 2) Mary budgeted $31 a day for her trip...

Stick Problem [05/13/1997]

Stick A is 8 cm longer than Stick B. Two thirds the length of Stick B is equal to half the length of Stick A. What is the length of Stick B?

Story Problems: Real, Realistic, Theoretical [10/24/2002]

I am trying to get the definitions for theoretical, realistic, and real problems to be able to determine different types of story problems.

Strategy: Finding a Formula [11/14/1997]

Jill needs three pieces of lumber a total of 27 ft. long for a dog pen. The second piece has to be 4 ft. longer than the first and the third 4 ft. longer than the second...

The Sum of Two Numbers is 20... [11/03/1997]

Twice one number is 4 more than four times the other. Find the numbers.

Sums in a Triangle [9/2/1995]

Six numbered bottle caps are arranged in a triangle. The sum of the three corner numbers, 1+6+5, is three more than the sum of the remaining numbers. How can you rearrange the bottle caps so that the sum of the corner number is twice the sum of the remaining numbers or the same as the sum of the remaining numbers?

Swimming Upstream and Down [09/19/1997]

A man swims 200 meters upstream in 3 minutes (180 seconds) and downstream 150 meters in .7 minutes. How fast is the man swimming and how fast is the water?

Syllables from One to One Million [03/12/2003]

How many syllables are there when counting from one to one million?

Tea and Cakes [11/13/2002]

A cafe sold tea at 30 cents a cup and cakes at 50 cents each. Everyone in a group had the same number of cups of tea and the same number of cakes. The bill came to $13.30. How many cups of tea did each person have?

Tea Blend: Price of Inferior Tea [6/24/1996]

6 kg of inferior quality tea are mixed with 3 kg of high quality tea. What is the price of the inferior tea?

Test Average Word Problem [02/20/2004]

In a certain class there are more than 20 and fewer than 40 students. On a recent test the average passing mark was 75. The average failing mark was 48 and the class average was 66. The teacher then raised every grade 5 points. As a result the average passing mark became 77.5 and the average failing mark became 45. If 65 is the established minimum for passing, how many students had their grades changed from failing to passing?

Three Freighters [10/11/1997]

Three freighters leave St. John's, Newfoundland, for Montreal, Quebec at the same time...

Three Pieces of Wire [01/07/1998]

A florist cuts a wire into 3 pieces. The 1st piece is 20% of the 2nd; the 3rd piece is 110% of the 2nd. The wire is 23 cm long; how long is each piece?

To Multiply or Divide? That Is the Question. [09/02/2003]

In a story problem, how do you know whether to multiply or divide?

Total Test Questions [09/21/1997]

On her biology test, Cathy answered 5/6 of the questions correctly...

Town Population [05/02/1997]

The population of town A is 4800 more than town B. If 3100 people move from town B to town A, the population in town A will be 11 times that of town B. Find the original total population of the two towns.

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