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A company sells 200 boat tickets for $50 each. For every $10 increase in the ticket price 5 fewer tickets will be sold.
Represent the number of tickets sold as a function of the selling price.
Represent the revenue as a function of the selling price.
Thanks to all who help.
Hi,
Ok, so at first for price=$50/ticket there will be 200 tickets sold and when the price goes $60/ticket there will be 195 tickets sold.
So the number of tickets (n) depends on the price (p). And we have
p n
50 200
60 195
70 190
...
It is linear : if you draw the function you see it (see figure). So, you calculate the slope for two of the points. Here, I chose (50;200) which is $50 -> 200 tickets and the point (70;190) which is $70 -> 190 tickets. So slope = (200-190)/(50-70) = -10/20=-1/2 so our linear function (y=mx+b) is y =
-1/2 x +b. We replace by the coordinates of (50;200) and we get 200=-1/2*50+b so b=200+25=225. So y=-1/2 x +225. Since our variables are p (the independent one) which is x and n which is y. We get n=-1/2 p + 225 (number of tickets sold as a function of the selling price).
(This function is only defined for price p between $50 and $450 because it begins at $50 and at $450 dollars n=-1/2*450+225=0 so after, n will ne negative which is impossible.)
Now, the revenue R is what they get in cash so for every ticket they get the price of the ticket in cash so they get n*p (if there are 200 tickets at $50 each they get 200*$50=$10000 in cash) so R=n*p (revenue as a function of the selling price).
So in general, Y as a function of X is Y=...x....... (Y=something expression containing x)
Wow thanks for the help. The imaged made it easier to understand. :D