# Averages

On this day in 1885 the Statue of Liberty arrived in New York Harbor. There were 350 pieces in more than 200 cases. The statue was designed by french sculptor Frederic-Auguste Bartholdi and was intended to commemorate both the American Revolution and a century of friendship between the United States and France. You can read more about the history of the Statue of Liberty here.

## 6/17 Averages

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

Alice bought m pens for n dollars each, and Ben bought n pens for m dollars each. Which of the following is the average price per pen, in dollars, for all the pens that Alice and Ben bought?

Remember that the first step in solving any math problem is to read the problem carefully. Next, you should identify the bottom line. For this problem, you are looking for " the average price per pen, in dollars, for all the pens that Alice and Ben bought." Before you start trying to solve the problems, always be sure to assess your options. Think about what you could do. In this case, you could write a formula, or you could pick numbers. Then think about what you should do. Since this is a fairly straightforward problem, it's probably best to just write a formula. Since the SAT is a timed test, you want to select the method that will get you to the correct answer in the least time. Now, all you need to do is calculate the average cost of the pens step by step.

Alice bought m pens for n dollars so she spent a total of m*n dollars and bought m pens. Ben bought a total of n pens for m dollars so he spent a total of n*m dollars and bought n pens. If we add up the total cost of the pens and divide that by the total number of pens purchased we have the following

$\frac{(m*n)+(n*m)}{m+n} = \frac{2mn}{m+n}$

Now, all you need to do is look at the answer choices and select the answer that matches your solution. Don't forget to loop back and verify that your answer matches the bottom line.

(A)

(B)

(C)

(D)

(E)

The correct answer choice is (B)

On sat.collegeboard.org 44% of the responses were correct.

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