<p>The average (arithmetic mean) cost of b books in a customer's online shopping cart is $24. The average cost of d DVD's in the same customer's online shopping cart is $16. If the average cost of all books and DVD's is $19, what is the value of d/b?</p>
<p>(24b + 16d)/(b+d) = 19, then solve for d/b.</p>
<p>Answer should come out to be 5/3, which makes sense because the average is closer to d than it is to b. The equation I gave you basically says that the average of 24(times amount of books) plus 16(amount of books) / (total amount of books) = 19.</p>
<p>Here’s another way to think about it:</p>
<p>When you want to take the average of two averages, you can’t just add them and divide by two. You have to take the “weighted” average.</p>
<p>They call them “weighted” averages for a reason. The “weights” are the number of items in each sub-group. And you can think of the overall average as the balance point on a see-saw. The one with more “weight” will be closer to the balance point. In fact, the distances and the weights are inversely proportional, just like masses on a see-saw.</p>
<p>So in this case, since the book average (24) is 5 away from the balance point (19) and the dvd average (16) is 3 away from the balance point, the weights must be in a 5/3 ratio as well – d being greater because its average was closer to the balance point.</p>
<p>I could say this example lets us leverage our physics knowledge…but that would be a pretty bad pun.</p>
<p>I got all the way until 5b = 3d.</p>
<p>How do I figure out what d/b is from here?</p>
<p>divide by 3b on both sides to get d/b = 5/3.</p>
<p>OR</p>
<p>Set either b or d to be equal to 1, solve for the other variable, then divide d by b.</p>
<p>For example,
When b=1
5(1) = 3d
5 = 3d
d =5/3</p>
<p>d/b = (5/3)/1.</p>
<p>you could have also set d =1 so:</p>
<p>5b = 3(1)
5b = 3
b = 3/5</p>
<p>d/b = 1/(3/5) = 5/3</p>
<p>^Awesome. Thanks for the help.</p>