13. Joining the frequent visitor program at the planetarium costs $5 per year, Write an equation that can be used to determine n, the number of visits per year for which the cost of being a member of the frequent visitor program is equal to the cost of not being a member. Tickets cost $11 for each student who is a member of the planetarium's frequent visitor program and $13 for each student who is not a member.
14 : Solve your equation from item 13. List a property of equality or provide an explanation for each step
15: Explain the meaning of the solution of the equation

- shreenithaa

- schrodinger

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- shreenithaa

hi do u know the answer to the questions
i need them by tomorrow morning at 5
thanks

- shreenithaa

can u start out by answering the first then i can do it on my own and finish the rest

- jennyrlz

hello :0

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## More answers

- shreenithaa

hi

- shreenithaa

my name is shree

- jennyrlz

Pleasure to meet you ^.^

- shreenithaa

u too

- shreenithaa

do u get the question, i am stumped

- jennyrlz

let me see... i will write as i read :)

- shreenithaa

k thanks for helping

- jennyrlz

planetarium program cost: 5 per yr
n=visits per year
perks for being a member: 2 dollars of ticket (non-memeber pirce: 13 dollars)

- jennyrlz

ok i got this information from number thirteen

- shreenithaa

k
did u get the answer

- jennyrlz

working it out xD

- shreenithaa

sorry take ur time

- jennyrlz

N = llx + 13y
hmm im a little confused by the question but this is what i got :)

- jennyrlz

X being the amount members visiting, and why the non members

- jennyrlz

and y*

- shreenithaa

that's what i got too but solving it was the hardest part i tried to search everywhere

- jennyrlz

to solve for it we would need to make up an x and a y

- shreenithaa

i think that x=13
and y=11 but how do you justify that that is your answer you know by using mathematical steps

- shreenithaa

it says that they have to be equal thats why

- jennyrlz

where does it say it has to be equal?

- shreenithaa

it says it on number 13

- shreenithaa

yup

- jennyrlz

ohhhhhhhhhhhhhhhhhhhh i see, i just skimmed it XD

- shreenithaa

its k

- jennyrlz

let me re make the equation then :)

- shreenithaa

k

- jennyrlz

11n = 13n

- jennyrlz

do you get it?

- shreenithaa

yeah but when it says n is the number of total visitors, it just gets confusing

- jennyrlz

ok let me explain it :)

- shreenithaa

thnx

- jennyrlz

n is the number of visitors, in other word total visitors not just members or vice versa. with me so far?

- shreenithaa

guess so

- shreenithaa

then how do you know how much n is

- jennyrlz

one sec let me finish explaining that then we will get to that :)

- shreenithaa

k

- jennyrlz

hmm let me make an analogy (a fictional example to help relate)

- jennyrlz

so if i were to try and get people to join a program i would try and show them the benefits, or how much money they can save correct?

- shreenithaa

yup

- jennyrlz

wait...

- jennyrlz

i just confused my self... let me step back andre think this from the beggining

- shreenithaa

sure

- jennyrlz

ok.. after some quick thinking ive come up with a new equation

- jennyrlz

5 + 11n = 13n

- jennyrlz

wow it makes sense now :D

- shreenithaa

yeah because of the +5 of the yearly thing but how about justifying it

- jennyrlz

with this equation we get 2.5 visits per year which is wrong.. but we are on the right tracks now!

- jennyrlz

lets make one more change to the equation

- jennyrlz

remebered i said N was the total visits correct

- jennyrlz

remember*

- shreenithaa

s remembering

- jennyrlz

this means that n can not be the same for both 11 and and 13

- shreenithaa

yeah beacuse not the same amount of people have membership and not so ur right

- jennyrlz

so the new equation is 5 +11x = N - 13y

- shreenithaa

okay

- shreenithaa

i just dont get how you will get n or x or y

- jennyrlz

hmm same... but lets ee

- jennyrlz

see

- shreenithaa

it would be easier if we knew what n was wouldn't we

- jennyrlz

hmm i just had an idea, let me try working it out on my side...

- shreenithaa

sure

- shreenithaa

i am sorry to hurry you but i need to go and could u type the answer i will check in the morning sorry i an stay for 10 minutes

- jennyrlz

Alright ill see if this idea leads to the answer :D

- shreenithaa

thns u have soooooooo much help

- shreenithaa

what grade r u in

- jennyrlz

12th

- shreenithaa

whaa... i am in 8th

- jennyrlz

but i finished highschool math last year xD

- jennyrlz

im taking college lvl math now ^.^

- shreenithaa

omg i have been waiting for colledge like forever

- shreenithaa

i cant wait to go

- jennyrlz

to think i passed calculus to be struggling on a middle school math problem u.u

- jennyrlz

college is fun :d

- shreenithaa

and hahaha well common core algebra 1

- shreenithaa

do u come home from colledge or stay there

- jennyrlz

go home

- jennyrlz

xD

- shreenithaa

oh guess that's why u r even here

- shreenithaa

gotta go

- jennyrlz

cya

- jennyrlz

I GOT ITTTTTTT

- jennyrlz

After many errors it all clicked!!!

- jennyrlz

we where right the first time! well... errr third time or whatever it was

- jennyrlz

the correct equation is 11n +5 = 13n

- jennyrlz

what we need to prove is that buying membership and paing 11 dolars or just not being a member is the same in this equation

- jennyrlz

so following the equation if you only go 2.5 times a year then it will cost you the same as if you buy membership and go 2.5 times a year

- jennyrlz

11(2.5) = 27.5
=27.5 + 5
=32.5
13(2.5) = 32.5

- jennyrlz

we did it!

- jennyrlz

i was mislead by the impossibility of visiting 2.5 times, but that doesn't matter, the question is just asking for an equation that would make it theoretically possible for them them to result in the same price!!

- jennyrlz

as for a property of equality...

- jennyrlz

we used the subtraction property of equaltiy

- jennyrlz

5+ 11n (-11n) = 13n (-11n)

- jennyrlz

subtraction equality means that if we subtract the same number to both sides we still end up with the same equations for example the equation 5=5, if we subtract the same numbeer from both sides, it will still be true. 2-5 =5-2 = 3=3

- jennyrlz

number 15 i think i answered by saying that you would have to visit 2.5 times etc....

- jennyrlz

wow that was hard! That is the most thinking ive done in a while hahaha,

- shreenithaa

thnx sooo much

- shreenithaa

u were really helpful i guess that finishing calculus really paid off huh

- shreenithaa

i finally got it and no u got the answer with the very little help i was able to give
thank u sooo much that was easier than i thought wow |dw:1441805152704:dw|

- jennyrlz

Np! It was fun :P

- jennyrlz

and nice art skills :D

- jennyrlz

And calculus is never worth it xD

- jennyrlz

i even reccomend taking statistics over precalc

- shreenithaa

thnx

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