<p>Ds did an SAT practice test and can't figure out how to solve this free-response question (and I certainly can't). I told him I'd post it here.</p>
<p>The average (arithmetic mean) of the test scores of a class of p students is 70, and the average of the test scores of a class of n students is 92. When the scores of both classes are combined, the average score is 86. What is the value of p/n (p divided by n)?</p>
<p>TIA</p>
<p>The average of the set of numbers: 10,20,30 is 20. If the numbers were not given, but it was stated that the average of 3 numbers is 20, it can be assumed that all three numbers are 20 (20+20+20/3 = 20). </p>
<p>In this case, it says: the average (arithmetic mean) of the test scores of a class of p students is 70. If the average is 70, you can assume that all the students scored 70. So if there were 10 students then the average would be (70X10)/10 = 70. (Total Points/ students) = average.
You can rewrite this as: 70p/p = 70. </p>
<p>The same goes for the second class: 92n/n = 92</p>
<p>When combining the scores, all you have to do is combine the total points scored by both classes and divide it by the total students.
So in this case that would be (70p + 92n)/(n+p) = 86
Cross multiply and you get 70p + 92n = 86n + 86p. Get the p's and n's on different sides and you get: 6n = 16p.
Divide by 16 on the left and divide by n on the right and you get 6/16 = p/n. Simplified: 3/8 = p/n</p>
<p>That's the right answer! Thanks so much. I'll print this out and see if it makes sense to him.</p>
<p>Try this, it is easier. p/n is just a ratio. you know that the average of p students is 70, 16 less than 86. You know that the average of n students is 92, 6 more than 86. Since you know that the ratio of the difference between the average and 70 and the average and 92 is 16/6, then you know that the ratio of the p to n must be the inverse: 6/16. Simplify this and you get 3/8. Simple.</p>
<p>I'll mention that to him. Definitely like things easy as possible. Thanks!</p>
<p>how come you had p next to 70 in: 70p/p=70 ? is it because you’re dividing that number/variable into 70 to get the number that was used to divide to get the mean in the first place?</p>
<p>@christyto
average = total sum/number of people
p = the number of people</p>
<p>therefore the average of the first class is 70p/p</p>