arithmetic mean

Question

Judi’s average (arithmetic mean) on four tests is 80. Assuming she can earn no more than 100 on any test, what is the least she can earn on her fifth test and still have a chance for an 85 average after seven tests?

Answer 1

Judi needs 7*85=595 points after seven tests

she has 4*80=320 points already

595-320=275 points needed on the next three tests

the highest she can get is 100 points on a test

275=100+100+75

the lowest score she can get is 75

Answer 2

These are the equations that we are currently looking at:

(a + b + c + d)/4 = 0.80

(a + b + c + d + e + f + g)/7 = 0.85

 

First, let's isolate the variables:

(a +b + c + d)/4 * 4 = 0.80 * 4

a + b + c + d = 3.2

 

and:

(a + b + c + d + e + f + g)/7 * 7 = 0.85 * 7

a + b + c + d + e + f + g= 5.95

 

Next, we can use the elimination method to get rid of the variables we don't need to worry about. Multiply the first equation by -1:

-1(a + b + c + d) = 3.2 * -1

-a - b - c - d = -3.2

 

and then subtract the first from the second to allow us to focus on the variables we need to worry about:

 a + b + c + d + e + f +g = 5.95

-a -  b -  c -  d                    -3.2

 

That leaves us with:

e + f + g = 2.75

 

100% is the highest, which is the same as writing 1, so we can plug those values into the other two tests:

e + 1 + 1 = 2.75

e + 2 = 2.75

 

And that leaves us with:

e = .75, or 75%