A student has scores of 70 and 80 on two tests. What must the student score on the last test to ensure that her average is greater than 80?

Her average is calculated by the mean, which takes the sum of all her scores and divides it by the number of steps.

Therefore, we just need to set up an inequality using the above formula. I'll call the third test 'x'.

First add all test scores together, divide by 3 and then use '>' to show the left side must be greater than 80:

(70 + 80 + x) / 3 > 80

Next, simplify everything. 70 + 80 can be simplified to 150:

(150 + x) / 3 > 80

Then multiply both sides by 3. The 3 on the left side cancels out as divide 3 and multiply 3 equals zero:

(150 + x) * 3 > 80 * 3

Now simplify everything again:

150 + x > 240

Now subtract 150 from both sides to isolate the x. 150 - 150 cancels out to zero:

150 + x - 150 > 240 - 150

Now simplify again and you have your answer:

x > 90

From rearranging the inequality, we have found that in her third test (x), she must score above 90 to have an average greater than 80.