Question

Davian enjoys going to the Planetarium and learning about the stars and planets. Each admission ticket costs $9.75. The Science Museum is having a special this week. If you donate $40 to the museum, then for the next year you only pay $4.75 for each ticket to the Planetarium.

The equations and graph below can be used to compare the cost paying full price for each ticket to the Planetarium to the cost of donating $40 to the museum and paying a discounted price for Planetarium tickets. In both the equations and graph, x represents the number of Planetarium tickets purchased and y represents the total yearly cost.

No Donation and Full-Price Tickets: y = 9.75x
$40 Donation and Discount-Price Tickets: y = 40 + 4.75x

How many times would Davian need to go to the planetarium for the yearly cost of the two different plans to be equivalent?

Answer 1

Assuming Devian goes to the planetarium every time he purchases a ticket,
the question is asking you when the yearly costs will be equal--
(yearly cost for both is "y").

The yearly cost w/o a donation and with full-price is y = 9.75x
The yearly cost with the donation is y = 40 + 4.75x

These are equal when x is...?

Answer 2

Or to rephrase, the y (yearly cost) of one is equal to the y of the other when x = ?

Answer 3

are you supposed to do an equation

Answer 4

Yes, create an equation where both of the yearly costs are equal. :)

Answer 5

so it would be 35.25?

Answer 6

No, that's not the answer. You're solving for "x" when y1 = y2.

Answer 7

this is too complicated for me -.-

Answer 8

nvm i got it thank you

Answer 9

:D Ah, okay.

Answer 10

What's your answer?