Writing Equations

8/19 Writing Equations

Read the following SAT test question and then select the correct answer.

Always take the time to read math questions carefully so that you will not make careless mistakes.  Identify the bottom line, which is the question you must answer, and assess your options for reaching the bottom line.  Choose the most efficient method to solve the problem and then attack it.  Do not forget to loop back and make sure that you solved for the bottom line, especially when you get a problem that requires multiple steps.

The price of 10 pounds of apples is d dollars. If the apples weigh an average of 1 pound for every 6 apples, which of the following is the average price, in cents, of a dozen such apples?

The bottom line that you are looking for is the cost of 12 apples in cents.  You can make a note of this by writing 12app = ¢?  Now ask yourself what you could do, and what you should do.  You could choose a number for the variable d and plug it into all of the answer choices, but then you would have to work several problems to find matching answers.  Instead, try working with the information you have, setting up the information in simple equations.

Your bottom line asks for the cost of 12 apples, but you were given information about 6 apples.  6 apples weigh 1 lb.  It is easy to change 6 to 12 by doubling it.

6 apples = 1 lb
12 apples = 2 lb

Now you have the dozen apples, so you must determine how many cents they cost.  You know that 10 lbs = d dollars.  Start by changing the dollars into cents, because you know you must end with cents.  To change dollars into cents, you must multiply the dollars by 100.

10 lb = d (solving for dollars)
10 lb = 100d (solving for cents)

Now you have the correct monetary unit, but you also still have an equation that solves for 10 lbs.  Your dozen apples is only 2 lbs.  To get from 10 to 2, divide both sides of your equation by 5.

10 lb = 100d
2 lb = 20d

Now put all the information that you have together to make sure that you solved for the bottom line:

12 apples = 2 lb = 20d

(A) (B) (C) (D) (E) The correct answer is (A).

On sat.collegeboard.org, 36% of responses were correct.

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