Lindsey has a test average of 80. On her next test, she gets a grade of 90, and her test average is now 82. How many tests has Lindsey taken in all?

Question

Lindsey has a test average of 80. On her next test, she gets a grade of 90, and her test average is now 82. How many tests has Lindsey taken in all?

Answer 1

LET T = the number of tests Lindsey took before the test where she scored a 90

We know Lindsey averaged 80 for all of the "T" tests.

This translates to 80T.

On her next test, she scored a 90.

This translates to 80T + 90.

After the test where Lindsey scored a 90, her test average is 82.

This translates to 82(T + 1).

Putting this together in an equation:

80T + 90 = 82(T + 1)

80T + 90 = 82T + 82 (Distributing)

80T + 90 - 82 = 82T (Subtracting 82 from both sides of the equation.)

80T + 8 = 82T

8 = 82T - 80T (Subtracting 80T from both sides of the equation.)

8 = 2T

4 = T (Dividing by 2 on both sides of the equation.)

But, T is the number of tests BEFORE the test where Lindsey scored a 90.

So, THE ANSWER IS 5. Lindsey took 5 TESTS IN ALL.

CHECKING:

Test 1 = 80, test 2 = 80, test 3 = 80, and test 4 = 80, since the average is 80.

(80 + 80 + 80 + 80) = 320 and 320/4 = 80

Test 5 = 90

(Tests 1-4 total) + test 5)/5 = (320 + 90)/5 = 410/5 = 82