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Middle School Archive

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Equivalent Expressions / Equivalent Equations [07/27/1997]

Could you please explain the difference between equivalent expressions and equivalent equations?

Escaping the Tiger [07/10/2003]

A man stands in the center of a circle. On the circumference is a tiger that can only move around the circle. The tiger can run four times as fast as the man. How can the man escape the circle without being eaten by the tiger?

Estate Distribution [05/10/1999]

Does 1/10 of the estate go to the church before or after taxes?

Estimating Seating Capacity [05/10/2000]

How can I estimate how many chairs can be placed in the seating area of a convention center meeting room that is 80 feet across at the front, 120 feet across at the rear, and 150 feet from front to back?

Evaporation [12/08/2003]

A substance is 99% water. Some water eveporates, leaving a substance that is 98% water. How much of the water evaporated?

Factoring vs. an Equation [10/01/2002]

The product of two consecutive odd numbers is 255. Find the numbers.

Farmer, Goat, Wolf, and Cabbage Cross a River [03/13/1998]

Fewest number of trips a farmer can make to get a goat, wolf, and cabbage across a river.

Feeding Chickens - Arithmetical Progression [7/6/1996]

A farmer has 3000 hens. Each week he sells 20... what is the total cost of feeding the hens...?

Fencing Two Back Yards [01/27/2001]

Sarah and Jane want to put a fence around their two rectangular back yards, with a single fence separating the yards... If they share the cost of the fence equally, how much will each of them pay?

Fibonacci and Possible Tilings [09/24/2003]

You are going to pave a 15 ft by 2 ft walkway with 1 ft by 2 ft paving stones. How does the Fibonacci sequence relate to the number of possible ways that the walkway can be paved?

Filling a Pool [07/28/1997]

It takes 2 hours to fill a pool with one hose, and 5 hours with another. How long does it take to fill the pool with both hoses?

Filling a Tank [08/01/1997]

How long will it take two pipes together to fill a tank?

Filling a Tank [12/19/2002]

A tank is filled by two pipes. The smaller pipe alone will take 24 minutes longer than the larger pipe and 32 minutes longer than when booth pipes are used. How long will each pipe take to fill the tank alone?

Filling a Tub [6/11/1996]

If one faucet fills a tub at a certain rate, and another faucet at another rate; how fast will the tub fill if both are open?

Filling Perfume Bottles [03/11/1997]

Three girls have a 24-ounce bottle of perfume which they want to divide equally among them. They have 3 empty bottles. How can they divide the perfume so that each girl has eight ounces in a bottle?

Find Depth of Water in a Tank [08/02/2003]

A rectangular tank measures 4m long, 2m wide and 4.8m high. Initially it is half full of water. Find the depth of water in the tank after 4000 litres of water have been added to it.

Finding a Formula for Mixtures [11/10/2003]

Alfredo needs to make 250 ml of a 27% alcohol solution, using a 15% solution and a 40% solution. How much of each should he use?

Finding Age in an Algebra Word Problem [12/8/1995]

Doris is as much older than Joris as Joris is older than Boris. Five years ago Doris' age was double what the age difference between her and Joris will be 15 years from now. How old is Boris?

Finding Ages: Tot and Teen [12/01/2002]

Tot is now half as old as Teenager was when Tot was a third as old as Teenager is now.

Finding an Equation for a Fish Word Problem [12/8/1995]

A boy breeds goldfish as a hobby. He decides to sell all his fish. He does this in five steps...

Finding a Number [4/13/1996]

My ones digit is twice my tens digit. One of my factors is 3. What am I?

Finding Integers Given LCM and GCD [11/05/2002]

The least common multiple of two positive integers is 144, and the greatest common divisor is 2. Neither integer is 2. Find both integers.

Finding Numbers Using Their Product [3/24/1996]

The product of two consecutive integers is 240. What are the integers?

Finding the Cost of Pets in a Pet Shop [2/26/1996]

In a large pet store, the sign above the fish tank says, "Buy sixteen fish and eight cats for the price of seven dogs"...

Finding the Cost of Washers in Relation to Bolts [12/8/1995]

Jacob Handyman has been told that 50 identical bolts and 20 identical nuts cost $9.10, whereas 30 nuts and...

Finding the Number of Fishbowls Sold [3/15/1996]

Trivia took some fishbowls to a flea market. In the first hour she sold one-third of them and a third more; in the second hour, she sold half of them and a half more; in the third hour she sold one-third and a third of one more; the next hour she sold half and half of one more; finally, she sold the last two. How many fishbowls did Trivia sell?

Finding the Weight of an Egg [2/9/1996]

If an egg weighs 20 grams and half an egg, what does an egg and a half weigh?

Finding Two Numbers with Known Product and Difference [08/06/2008]

Two numbers have a product of 6800 and a difference of 5. Find the numbers. How can I solve this without using algebra?

Finding Units [4/14/1996]

The two digits in the numerator of a fraction are reversed in its denominator. If 1 is subtracted from both the numerator and the denominator...

Find the Angles [9/11/1996]

The first angle of a triangle is eight degrees more than two times the third angle. The second angle is two degrees less than three times the third angle. Find all three angles.

Find the Heavier Coin of 12 in 3 Weighings [11/17/1996]

If there are twelve coins in a bag, one of which is either lighter or heavier than the others, find the fake coin in exactly 3 weighings AND determine if it is lighter or heavier than the others.

Find the Numbers [08/28/2003]

One number is 61 more than a second number. The sum of the two numbers is 127. Find the numbers.

Five Bags of Nuts [04/17/2002]

Given 100 nuts in five paper bags, in the first and second bags there are altogether fifty-two nuts; in the second and third there are forty-three; in the third and fourth, thirty-four; in the fourth and fifth, thirty. How many nuts are there in each bag?

Football Scoring [11/24/2002]

What was the number of points scored by the red team? What is the smallest number of scoring plays that the red team could have made to get its point total?

For a Given Number, Solve the Expression... [6/28/1996]

For a given number m, m greater than or equal to 1 , solve: The square root of m + x plus the square root of m - x divided by the square root of m.

Formulas and Missing Quantities [10/09/2004]

Variations on the question "Could you drink enough water in a lifetime to empty a pool?" lead to a discussion of using formulas to find missing quantities.

Four Methods of Solving Classic Chicken and Egg Problems [02/24/2009]

If 6 cats can kill 6 rats in 6 minutes, how many cats will it take to kill 100 rats in 50 minutes? A look at four different solution methods for this sort of problem.

Fractions and School Enrollments [02/26/2003]

The sum of 1/2, 1/3, and 1/4 of the enrollment of the Business School is exactly the enrollment of the Language School. The sum of 1/5, 1/6, 1/7, and 1/8 of the enrollment of the Business School is exactly that of the Design School. What are the enrollments of these three schools, assuming no school has more than 1000 pupils?

Fractions: Sheets of Paper Left [08/07/1997]

An office got a new copier and was given 800 sheets of paper. On the first day they used 1/3 of the paper...

From Word Problems to Equations [01/28/1999]

If the sides of a square are lengthened by 3m, the area becomes 81m squared. Find the length of a side of the original square.

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