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Word Problems

Browse Middle School Ratio/Proportion
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Mixture problems.
    Unit conversions, unit cancellation.
    What is a ratio?

Two Numbers in 5:3 Ratio [12/07/2002]
Two numbers have a ratio of 5:3. The larger number is 36 more than half the difference of the two numbers. What are the two numbers? There are two pairs of numbers that will make this a true statement. You need to find both of them.

Using a Diagram to Find a Formula [11/13/2002]
A bag contains green, yellow and orange marbles. The ratio of green to yellow marbles is 2:5. The ratio of yellow to orange marbles is 3:4. What is the ratio of green marbles to orange marbles?

Using Estimation to Check Your Answer [03/28/2008]
I had to find the percent increase in population from 38,000,000 to 515,000,000 and I got 1,255%. But that seems way too big. Where am I going wrong?

Using Scale Drawings [05/24/2002]
Use a scale drawing to determine the actual size of an object.

Variation on Combined Work [06/13/2002]
If you run a large pipe for 4 hours, and run a small pipe for 9 hours, you can fill 1/2 a pool. If you run both pipes together for 12 hours, you can fill the whole pool. How long would it take to fill the pool using each pipe by itself?

Visualizing Ratios to Scale Least Common Multiples [10/02/2010]
The ratio of Cotsworld sheep to Swaledales is 3:5, and the ratio of Swaledales to Longwools is 7:4. What is the ratio of Cotsworlds to Longwools?

Weighted Averages [11/30/2001]
An advertisement for an orange drink claims that the drink contains 10% orange juice. How much pure orange juice would have to be added to 5 quarts of the drink to obtain a mixture containing 40% orange juice?

Which is More? [05/21/2002]
Given a choice between nickels stacked to your height, or quarters placed end to end to your height, which should you choose?

Why Does Cross Multiplication Work? [05/09/2002]
Why does the rule a/b = c/d also mean ad = bc? Why can we solve proportions by cross multiplying?

Why There are 12 Tones in a Scale [12/28/2000]
Why are there 12 tones in an octave? Can you explain the significance or the equation r^n = 2^m? Also, what's so special about a fifth? Why should the scale be based on the fraction 3/2?

Working with Multi-Part Ratios [05/21/2007]
Can you explain how to work with a three-part ratio such as 2:3:6? I understand basic ratios but am not sure how the various numbers relate to each other when there are more than two of them.

Writing Ratios [06/03/1999]
How can I write a ratio in three different ways?

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