Question

I am...confused.

The average (arithmetic mean) of n and 3 is equal to the average of 7 and 5. What is the value of n ?


(A) 7
(B) 8
(C) 9
(D) 10
(E) 12

Answer 1

equate the two and solve for n

Answer 2

How do you find the average of two numbers?

Answer 3

you add them...then divide by the amount of numbers added. (I think)

Answer 4

Right. Add the numbers and divide by 2 (in our case).

Answer 5

Can you write an expression of the average of 7 and 5?

Answer 6

since you divide by 2 in each case, its only the adding thats key

Answer 7

7+5=12/2=6 e.e

Answer 8

a/2 = b/2 implies a=b

Answer 9

The expression for the average of 7 and 5 is:

\(\dfrac{7 + 5}{2} \)

Right?

Answer 10

yes o.o

Answer 11

The expression of the average of n and 3 is:

\(\dfrac{n + 3}{2} \)

Since we are told the averages are equal, you set the two expressions equal:

\(\dfrac{n + 3}{2}\ = \dfrac{7 + 5}{2} \)

Now you need to solve for n.

The first step is to add the 7 and 5 in the right numerator.
Then multiply both sides by 2. That gets rid of the denominators.
Then subtract 3 from both sides to find n.

Answer 12

Wait...I thought I understood and I was gonna say the answer is C.9 but I'm lost at the last two steps that you just stated...

Answer 13

Here is the *important* idea
\[ 2 \cdot \frac{1}{2} = \frac{2}{2}= 1\]

or if you start with
\[ \frac{x}{2} \]
you can write that as
\[ \frac{1}{2} \cdot x \]

now we use the important idea: if we multiply by 2 we get
\[ 2 \cdot \frac{1}{2}\cdot x = 1\cdot x = x\]

Answer 14

For your problem,
\[ \dfrac{n + 3}{2}\ = \dfrac{7 + 5}{2} \]
you can "get rid" of the 2 in the bottom by multiplying by 2 up top (this is the important idea)

but with an equation, to keep things equal, you have to do the same thing to both sides. So multiply both sides by 2:
\[ 2\cdot \dfrac{n + 3}{2}\ = \dfrac{7 + 5}{2} \cdot 2\]
notice we have
\[ \frac{2}{2} \cdot (n+3) = (7+5) \frac{2}{2} \]
(the 2/2 is 1 , which is why we multiplied by 2... it makes 2/2, and that is 1)
in other words:
n+3 = 7+5

now solve for n
the next step is add -3 to both sides.
then simplify.