If the average of four numbers is 22, and three of the numbers are 7, 11, and 18, then what is the fourth number?

Question

anonymous · Answer

52 because 52+11+7+18= 88
and 88 divided by 4 = 22

mathmale · Answer

average = (sum of all the numbers) / (count of the numbers...how many there are).

Here we know the average is 22, and we know 3 of the 4 numbers, so we represent the fourth number by x.

Add up the four numbers.

Sum of the numbers is:   ????
How many numbers are there?    ????
Divde the sum by the count.

Equate the result to the average (22).  How would you now solve for x?

mathmale · Answer

Isaiah, why the x in the denom.?

mathmale · Answer

Isn't the average = to 22?

anonymous · Answer

$$\frac{1}{4} (x+18+11+7)=22 $$x = 52

mathmale · Answer

Nice work, Robert.  But you might want to lead Megan through the steps involved here.

jagatuba · Answer

$$\frac{ 7+11+18+x }{ 4 }=22$$

mathmale · Answer

Again, right on.  But how do you solve this equation for x?  Megan may want to know.

mathmale · Answer

(For jagatuba only:  Thanks for referring me to Preetha a week or so ago.  I did contact her and find her to be very helpful!)

anonymous · Answer

@megan177
The average of n numbers is the sum of the n numbers divided by n.

jagatuba · Answer

$$36+x=22\times4$$
$$x=88-36$$

mathmale · Answer

Right on.  But what about the algebraic steps involved in solving that equation for x?

mathmale · Answer

Cool, Jag!  Megan, how are you doing?

jagatuba · Answer

@mathmale YW. Glad she could help.

mathmale · Answer

Thanks.

Megan?  Still with us?

mathmale · Answer

@megan177 ?

anonymous · Answer

Megan is "off line"

anonymous · Answer

relax I was off line, my computer froze. okay I get it now, thanks guys