Can someone help me with this problem and the steps involved?

Question

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

I got 77%, but I don't know the equation. I just kept using different numbers until I came up with 77%.

Answer 1

OK, consider that each exam counts 20% of the final score. So the grade is 0.2*(79 + 56 + 91 + 72 + S), where S is the score on the last test. Multiplying that out, you get that the grade = 59.6 + 0.2S. Now you want the grade to be at least 75, so say 75 = 59.6 + 0.2S. Subtract 59.6 from each side: 15.4 = 0.2S. Now multiply each side by 5: 77 = S.

Answer 2

This problem is an inequality. You want to know which scores will result in an average of 75 or higher. Therefore, the answer will be expressed as being "greater than or equal to" a certain number. Here is how I would solve it:
(79 + 56 + 91 + 72 + x) / 5 >= 75
(298 + x) / 5 >= 75
[(298 + x) / 5] * 5 >= 75 * 5
298 + x >= 375
298 + x - 298 >= 375 - 298
x >= 77
So, you were right. Any percentage above 77 would give an average of 75 or higher.

Answer 3

Remember that the formula for the average of 5 numbers goes as follows.

V = (a + b + c + d + e)/5

We're given the scores of 4 tests, so we'll substitute those for a through d, and use an unknown x for e.

V = (79 + 56 + 91 + 72 + x)/5

We also know that V must be at least 75, so let's calculate it AT 75 and see what we get as a minimum value.

75 = (79 + 56 + 91 + 72 + x)/5

Then it's basic algebra. Multiply both sides by 5 to get:

375 = 79 + 56 + 91 + 72 + x
375 = 298 + x
375 - 298 = x
Therefore x = 77

Answer 4

Let's define the equation:

Mean = ((score 1) + (score 2) + (score 3) + (score 4) + (score 5)) / 5

{divided by 5 because there are 5 scores total}

If we know we want a mean of 75 and we have four of those scores, we can plug them into the equation.

75 = (79 + 56 + 91 + 72 + score 5) / 5
75 * 5 = ((79 + 56 + 91 + 72 + score 5) / 5) * 5 (multiplied BOTH sides by 5
375 = 79 + 56 + 91 + 72 + score 5
375 = 298 + score 5
375 - 298 = 298 + score 5 - 298 (subtracted 298 from both sides)
375 - 298 = score 5
score 5 = 77

Double check your work! Plug in 77 into original equation:
75 = (79 + 56 + 91 + 72 + 77) / 5?
75 = 375 / 5? yes! therefore, correct!

Answer 5

Its best to convert everything from averages to totals.
The total so far is 79+56+91+72 = 298. An average of 75 over 5 exams means a total of 75*5 = 375.
Thus, the student must score at least 375-298 = 77%.

Answer 6

The equation would just be 79+56+91+72+77=375 then divide that by 5 which = 75
But, if your teachers tells you to round then the answer would be 75 instead of 77 bceause 75 would give you an anverage of 74.6.
So it would be 79+56+91+72+75=373 and divided by 5 would be 74.6

Answer 7

Current aggregate = 79 + 56 + 91 + 72
= 298

If average ≥ 75 after 5th exam,
then aggregate ≥ 75 x 5 (as average = aggregate / 5)
= 375

Let the student's next score be s%

So 298 + s ≥ 375

So s ≥ 77

ie The student's next score must be AT LEAST 77

Answer 8

Lets call your unknown score s.
(79+56+91+72+s)/5=75. Mutilpy through by 5 to get rid of thar fraction
79+56+91+72+s=5x75=375 then subtract all of the other scores from both sides of the equation to get s all by itself over there on the left side of the = sign:
s=375-79-56-91-72=77
. Algebra is just a few steps you take to get the unkowns on one side of the equation and the knowns on the other side of the equation. You look at the equation with its unknowns and figure out what has been done to it to mix all those other numbers with the unknown, and do the opposite things (multiply to undo division, divide to undo multiplication, add to undo subtraction, subtract to undo addition) to get the unknown by itself on one side of the equation and a simple arithmatic problem on the other side of the equation.
. When there are multiple unknowns, you can only solve if you have as many independant equations (equations which are not simple mutiplcations of each other) as there are unknowns. Then you treat all of the unknowns except for one as if they were knowns, and go through one equation at a time, substituting what you found the unknown (which was treated as an unknown) to be for that unknown in the next equation. As you do this for one equation after another, you finally get down to a simple numerical answer for tha last unknown, Then go back and plug it into the preceding equation to figure ot the value of that unknown. Each step that you go back through the eqations converts an unknown into a simple number. When you get back to the first equation, you have converted all of the unknowns into numbers.

Answer 9

equation is (79+56+91+72+X) divided by 5 is equal to or greater than 75. I think!

Answer 10

Okay, first we want to know what the average of the first four scores is. You know how to do that, don't you?

To find the average you take the samples (in this case, our test scores) and add them together, then divide by the number of samples (in this case, four) So that would be 298/4

Since we are going to add another sample to the group, we will be dividing by five next time. So what we want is:

75 = X/5 solve for X

x = 5(75), or 375.

375 - 298 leaves 77, so that is how large the fifth sample must be.

3 DEC 06, 2102 hrs, GMT.