## Thursday, September 5, 2013

### Percent word problems set two.

Percent word problems -- set two.

This problem builds on the issue presented percent word problems set one.

Question:

A student has taken four tests   Her grades so far are 80 out of 100, 30 out of 50,  120 out of 125, and 88 out of 100.   The student gets 95% on her final exam.  How many points are on the final exam if her final percentage for the quarter is 90.0%.

Hint:

Students unfamiliar with the concept of percentage may want to go to the Khan web site and watch some videos.  Here is a link.

Denote the number of points on the final exam as N.   This means the student got 0.95xN points on the test.

The fraction correct for all five tests is

0.90=(80+30+120++88+0.95xN)/(100+50+125+100+N)

0.90= (318+0.95xN)/(375+N)

This simplifies to

0.90 x 375 + 0.90 x N = 318 + 0.95 x N

337.5 + 0.9 x N = 318 + 0.95 x N

19.5 = 0.5 x N

or

N=19.5/0.05 = 390

Note that (0.95*390+318)/(375+390) is equal to 0.90.

You may have already looked at percent word problem set one.  If not here is the link.

This post on why the percent down is not equal to the percent up was very popular.

I find the use of Khan combined with new problems an effective way to present material.  I will create more web sites linking Khan to my math problems.