Tino conducted a survey of all the eighth graders in his school for his math project.He asked each student how much he or she spent on school supplies at the beginning of the year (rounded to the nearest dollar) he also caculated the average amount spent and found it to be $15.50 unfortunately,it rained on the day he brought the graph to turn it in,and the last bar got smudged.What is the height of the smudged are?

Question

anonymous · Answer

http://edweb.tusd1.org/gververelli/Algebra%20Stuff/POTW/POW09.htm

anonymous · Answer

go to this link and and scroll down youll see the graph

anonymous · Answer

@IMStuck

anonymous · Answer

@amistre64

amistre64 · Answer

take a weighted average

amistre64 · Answer

or ... sum xP(x) is the same thing

anonymous · Answer

did you find the problem on the link @amistre64

amistre64 · Answer

$$\frac{a\alpha+b\beta+c\gamma+d\delta+...+k\kappa}{a+b+c+d+...+k}$$

amistre64 · Answer

i found it, we need to take a weighted average

anonymous · Answer

um im in 8th grade

anonymous · Answer

can i tell you what my teacher gave me

anonymous · Answer

for an equation @amistre64

amistre64 · Answer

only if its sensible ...

anonymous · Answer

total spent + 20x
--------------                  18(12)=216       20(13)=260
number of kids + x

amistre64 · Answer

ideally, if we add up all the amounts that each kid gave, and divide by how many kids gave an answer .... we have an average.

18 kids gave 12:  12+12+12+12+12+ ... or 18(12)
20 kids gave 13:  13+13+13+ .. or simply 13(20)
21 kids gave 14:  14(21)

see how its working?

anonymous · Answer

yes thats what he wanted us to do but i dont see how its working @amistre64

amistre64 · Answer

$$\frac{18(13)+ 20(14)+ 21(15)+ 22(16)+ 18(17)+ 16(18)+ 8(19)+ 10(20)+ x(21)}{18+20+21+22+18+16+8+10+x}\
=15.50$$

amistre64 · Answer

i mis saw something in there trying to flip between pages

amistre64 · Answer

but thats the basic premise.

amistre64 · Answer

oh, we start at 12, not 13

amistre64 · Answer

$$\frac{18(12)+ 20(13)+ 21(14)+ 22(15)+ 18(16)+ 16(17)+ 8(18)+ 10(19)+ x(20)}{18+20+21+22+18+16+8+10+x}$$
simplify that for me

anonymous · Answer

this might take awhile @amistre64

anonymous · Answer

hold on

amistre64 · Answer

while your pondering it ... do you agree that an average is simply the sum of the number of items, divided by how many items there are?

anonymous · Answer

yes

amistre64 · Answer

then thats really all we are doing here.  but being smarter about it

18 kids gave $12  if we add 12 to itself 18 times ... thats the definition of multiplication:
    18(12)

the top part is just summing up all the money that was given by taking the frequency of each dollar amount instead of adding them up one by one

amistre64 · Answer

the bottom is therefore how many kids gave in the first place ... 

18 gave this
20 gave that
21 gave those
22 gave something else ....

the sum of the number of kids is the bottom

anonymous · Answer

2024x
------- = 15.
133z

anonymous · Answer

@amistre64

amistre64 · Answer

1994 + 20x
----------- = 15.50
  133 + x

solve for x

anonymous · Answer

how did you get 1994

anonymous · Answer

i got 2024

anonymous · Answer

did i add wrong

amistre64 · Answer

http://www.wolframalpha.com/input/?i=18%2812%29%2B+20%2813%29%2B+21%2814%29%2B+22%2815%29%2B+18%2816%29%2B+16%2817%29%2B+8%2818%29%2B+10%2819%29 i made the wolf do the calcualtions for me

anonymous · Answer

oh k

amistre64 · Answer

there was not way i was going to chk that by hand :)

anonymous · Answer

i put it in the caculator and got 2014

amistre64 · Answer

you might need new batteries

amistre64 · Answer

so lets assume we did this right:

18(12)+ 20(13)+ 21(14)+ 22(15)+ 18(16)+ 16(17)+ 8(18)+ 10(19) + 20x

1994 + 20x on top

and

18+20+21+22+18+16+8+10 + x 

133 + x on the bottom

anonymous · Answer

its 2,014 i used the google caculator but i didnt add the ask just 20

anonymous · Answer

but its 2014x

amistre64 · Answer

using m for the mean

1994 + 20x = m(133+x)

1994 + 20x = 133m + mx

20x - mx = 133m - 1994 

x(20 - m) = 133m - 1994 


        133m - 1994 
x =  ------------
             20 - m

amistre64 · Answer

you can add unlike terms ... 20x  is not able to be added for starters.  it has to be worked in seperately

amistre64 · Answer

if you want to use your findings, feel free ....

anonymous · Answer

1994 + 20x
----------- = 15.50
  133 + x

amistre64 · Answer

yep .... i used m for a simpler run thru

anonymous · Answer

im confused on wht to do

amistre64 · Answer

using m for the mean

1994 + 20x = m(133+x)

1994 + 20x = 133m + mx

20x - mx = 133m - 1994 

x(20 - m) = 133m - 1994 


        133m - 1994 
x =  ------------
             20 - m

anonymous · Answer

oh ok

anonymous · Answer

you wnat me to solve

anonymous · Answer

@amistre64

amistre64 · Answer

yes, i want you to solve

anonymous · Answer

do i have to use the m

anonymous · Answer

@amistre64

amistre64 · Answer

what does m equal in this case?  i defined it to make my life simpler

anonymous · Answer

mean i was just asking i thought i could use x

amistre64 · Answer

x is what is not known :)  m is known, just easier for me to work with when moving things about

anonymous · Answer

oh ok

anonymous · Answer

15.0

anonymous · Answer

@amistre64

amistre64 · Answer

x = 15 is what i get as well

anonymous · Answer

so that was it

amistre64 · Answer

with any luck yes :)

i would not have attempted that by hand, which is why i trust the wolf on it

anonymous · Answer

oh thank you finally finished

anonymous · Answer

thank you so much @amistre64

amistre64 · Answer

youre welcome :)