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Critical Thinking: evaluating information

by Tom
(Flordia)











































Critical Thinking

A brick balances exactly with 3/4 of a pound and 3/4 of a brick.

What is the weight of a brick in pounds?

Comments for Critical Thinking: evaluating information

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Nov 17, 2012
Critical Thinking
by: Staff



Answer

Part I

This problem can be solved using ratios because the ratio of the weight of bricks to the number of bricks will be a constant proportion.

This is an excellent question because ratios and proportion can be applied to many routine problems encountered in everyday life. Ratios allow you to compute unit prices, projected cost, projected weight and volume, quantity of cooking ingredients, and solve many other common problems.

I am going to spend a little more space on the preliminary explanation because ratios are so useful.

For example, when shopping for the best value of a particular item, ratios will allow you to compare unit prices between items sold in different quantities.

Suppose you are shopping for a particular kind of breakfast cereal. If you are comparing the prices for boxes with different quantities (say, a 48 oz versus 35 oz box), ratios will allow you to compute prices per ounce.

Suppose you are shopping for small bundles of firewood. If you need to compare the prices for different quantities (say, .75 ft³ versus 1.5 ft³), ratios will allow you to compute prices per ft³.


Direct Proportions:

         A direct proportion between two variables means that one variable is a constant multiple of the other variable.

         The terms “proportional relationship”, “direct variation” and “direct proportion” all mean the same thing. The terms are interchangeable.

         The equation for a “proportional relationship” ALWAYS looks like this:

             y = kx

         k is a constant. It is called the “constant of variation”.


      I’m going to rearrange that equation so it looks like this:

             y/x = k

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Nov 17, 2012
Critical Thinking
by: Staff


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Part II

         In other words, a direct proportion means that DIVIDING the value of ONE VARIABLE BY THE value of the OTHER variable is a CONSTANT value (k, the constant of variation). (I’ll apply this idea to your problem shortly).

         For example, if you have a job and are paid by the hour, your pay is proportional to the number of hours you work.

             The more hours you work, the higher your pay.

             The fewer hours you work, the lower the pay.

             However, your total pay divided by the total number of hours you work is a constant value.

             If your rate of pay is $25 per hour and you work 10 hours, you will earn $250.

             $250 ÷ 10 hours = $25 per hour

             If your rate of pay is $25 per hour and you work 1000 hours, you will earn $25,000.

             $25,000 ÷ 1000 hours = $25 per hour

             Pay divided by hours always EQUALS the same number, the CONSTANT of variation. In this example the constant of variation is 25. The constant of variation (25) will not change, regardless of the number of hours you work.

         The equation for computing the weight of one brick in your problem statement is the same equation discussed in the preceding paragraphs. It will look like this:

             y = kx

             (weight of bricks) = k * (number of bricks)


             You need to calculate k, the constant of variation. That is the answer to your question..


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Nov 17, 2012
Critical Thinking
by: Staff


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Part III


             The constant of variation brick is:

             (weight of brick) / (number of bricks) = k

             Since the problem statement presents ¾ of a brick with a weight of ¾ pound:

             (¾ pounds) / (¾ of a brick) = k

             (¾ pounds) / (¾ of a brick) = 1

             k = 1


         The final equation is:

             (weight of bricks) = k * (number of bricks)

             (weight of bricks) = 1 * (number of bricks)

         For the sake of simplicity, let w = “weight in pounds” and n = “number of bricks”:

             w = 1 * n

             w = 1n


             when n = 1

             w = 1 * n

             w = 1 * 1

             w = 1

Final Answer:

1 brick weighs 1 pound







Thanks for writing.

Staff
www.solving-math-problems.com



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