# Ella has an average score of 82 on three tests.  Her average score on the first two was 85.  What was her score on the third test?

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quirozd | Certified Educator

Answer: c = 76

Remember that average is just the sum divided by the number of items summed. We can use ratios to help us see the answer. Let a, b, and c, be the scores of the three tests (I know, original!).

So Equation 1 is: `(a+b+c)/3 = 82`

and Equation 2 is: `(a+b)/2 = 85`

Let's rearrange to get c by itself in equation 1, and the quantity a+b by itself in equation 2.

`3times(a+b+c)/3 = 3times82` Multiply both sides by 3

`a+b+c-(a+b) = 246-(a+b) ` Subtract a and b from both sides

Eq. 3: `c=246-(a+b)` Rewritten to see a+b as an expression. Why? See the next step.

Starting with equation 2:

`2times(a+b)/2=2times85` Multiply both sides by 2

`a+b = 170` .

Now go back and replace (a+b) with 170 and solve.

`c=246-(a+b) `

`c=246-(170) `

`c=76 `

Evaluate: Does it make sense? If your test average was 85, and then you got a 76, it should bring the overall average down - since you did below the average. How much it brings it down depends on the number of tests taken. If it was just two tests total, the overall average would have gone to 80.5. If it were four tests total, the overall average would have only gone to 82.75.

Answer: c=76

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