Thread: Calculating grade

i am lost after i add 79,56,91,72 i divide by 4 after this is were i am stuck can you help me out i learn better if i can see the steps just once. here is the problem:

A student has made a 79, 56, 91 and 72 on four tests. Determine the possible scores on the fifth test that will result in a 75 or higher average (assume an average cannot go higher than 100)…Hint: set up an inequality to calculate the grade if the average would be between 75 and 100.

A student has made a 79, 56, 91 and 72 on four tests. Determine the possible scores on the fifth test that will result in a 75 or higher average

The score on the fifth test we will call 'x'

so the average after the fifth test will be:

(79 + 56 + 91 + 72 + x)/5
or

(298 +x)/5

or

59.6 + x/5

so what we want is:

75 <= 59.6 + x/5

15.4 <= x/5

77 <= x

In order to get at least a 75, the student needs to score a 77 or higher.

Here is one way.

If there are 5 test in total, then the average grade is the sum of the 5 grades divided by 5.

75 <= (79 +56 +91 +72 +x)/5 <= 100
75 <= (298+x)/5 <= 100
Clear the fraction, multiply all sides by 5,
375 <= 298 +x <= 500
Isolate the x, subtract 298 from all sides,
77 <= x <= 202

That means on the 5th test, the student must score anywhere between 77 and 202.

Can a grade or test score be more than 100?
If not, then the 5th grade should be anywhere from 77 to 100.