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# Averages

## How do we calculate averages?

Average is the result of adding all numbers in a set then dividing by amount of numbers.

##### Example 1

The average of 1 and 5 is 3, because $$(1+5)/2= 3$$

##### Example 2

The average of 1, 5, and 9 is 5, because $$(1+5+9)/3=5$$

### Practice Problems

##### Problem 1

E. $$70$$

$$3*60=180$$, which is the total number of points earned.

The two numbers we do know are $$50$$ and $$60$$ which add up to $$110$$.

The third number is $$180-110=70$$ since all three numbers must add up to $$180$$.

TEST METHOD: AVERAGE PIE

Use the average pie to chart out what you know and simplify this problem.

##### Problem 2

E. $$54$$

$$x+y=90$$ since the other angle is $$90°$$ and a triangle has $$180°$$ in total.

The two numbers we do know are $$50$$ and $$60$$ which add up to $$110$$.

The third number is $$180-110=70$$ since all three numbers must add up to $$180$$.

TEST METHOD: AVERAGE PIE

Tip: Total degrees = $$180+180=360$$, the total number of degrees in two triangles.

##### Problem 3

C. Two

METHOD: AVERAGE PIE. You know the total $$(5*80=400)$$. You know the number ($$5$$), and you know the average ($$80$$). You also know the answer is between $$0$$-$$4$$. By trial and error you should be able to answer this one.

KEYWORDS: "greatest possible", "inclusive"

If you're clueless, NO MATTER what you should be able to eliminate A and guess. If you couldn't eliminate A, review how to solve average problems.

##### Problem 4

A. $$(a+c)/2$$

TEST KEYWORD: "MUST"

Plug in numbers for $$a$$, $$b$$, $$c$$ and see which answer 'must' work.

##### Problem 5

A. $$0$$

Eliminate some obvious wrong ones B, C, E. Remember to always estimate and have a good rough estimate of where the answers should be which is right around the original average of $$9$$; if you added a new number that was much higher or lower like say $$0$$ or $$1,000$$ the average could never remain $$9$$.

TEST TRAP: D is a trap and since you're not dealing with the first few problems you should not have gone on without really thinking about his one.