How many magazines did the school library subscribe in December?

Question

A school library spends $80 a month on magazines. The average price for magazines bought in January was
70 cents more than the average price in December. Because of the price increase, the school library was forced
to subscribe to 7 fewer magazines. How many magazines did the school library subscribe in December?

Answer 1

Hi Melissa,

 

Thanks for sharing your math problem. I went over it and found it to be tricky. 

 

To solve this problem, we need to establish two things:

1. The average price for magazines is defined as the price per number of magazines. 
2. Assume the school library pays $80 in both December and January. 

 

That said, now we can work out the details. 

 

Step 1: Determine the equations in the word problem.

 

The first thing you need to do is write the equations for the average price, and the number of magazines purchased. The equation for the average price can be determined using the second sentence. The third sentence will give you the equation for the number of magazines purchased. 

 

Step 2: Convert the number of magazines purchased to an average price ( price per number of magazines)

 

This part is tricky. After you create your equation for the number of magazines purchased in January, you'll need to convert the equation to the price per number of magazines. Remember the second assumption we made? We need to assume the library continued to pay $80. That said, you'll end up with a rational expression. 

 

Step 3: Convert the average price equation to the price per number of magazines 

 

Step 4: Rearrange equation to solve the number of magazines purchased

 

When you rearrange this equation, you should have a quadratic expression. You'll need to factor it in order to find the solution for this problem. 

 

 

This problem is conprehensive. If you get lost or stuck, I recommend setting up a session so that we can go over it in more detail.

 

Thanks for using Answers,

 

Have a great evening

 

Ouray