The Downhill Ski club is organizing a ski trip. Group tickets for the ski trip are priced at $20 for the first 100 skiers and a discount of $5.00 per ticket for each of the skiers over 100.
a) write a formula to find the cost of x skiers.
Answer: c(x)=2000+15(x-100), if x>100
b) How many skiers need to go to bring the price per ticket to $16.00.
You got part (a) correct.
For (b), solve:
2000+15(x-100) = 16 x
x = 2000 -1500 = 500
400 of the 500 skiers get $15 tickets.
Total revenue is 6000 from them and 2000 from the first 100, or $8000. That is an average of $16 each.
To find the number of skiers needed to bring the price per ticket to $16.00, we can set up the equation:
$16.00 = $20.00 - ($5.00 * (x - 100))
Where x represents the number of skiers.
Simplifying the equation:
$16.00 = $20.00 - $5.00x + $500.00
Moving the terms around:
$5.00x = $500.00 - $20.00 + $16.00
$5.00x = $496.00
Dividing both sides by $5.00:
x = $496.00 / $5.00
x = 99.2
Since we cannot have a fraction of a skier, we can conclude that we will need at least 100 skiers to bring the price per ticket to $16.00.
To find the number of skiers needed to bring the price per ticket to $16.00, we can set up an equation using the formula from part (a).
Let's set up the equation:
c(x) = 2000 + 15(x - 100)
We want the cost per ticket to be $16.00, so we can replace "c(x)" with 16:
16 = 2000 + 15(x - 100)
Now, we can solve for x:
16 - 2000 = 15(x - 100)
-1984 = 15x - 1500
-1984 + 1500 = 15x
-484 = 15x
Dividing both sides by 15:
-484/15 = x
x ≈ -32.27
Since we can't have a negative number of skiers, we round up to the nearest whole number.
Therefore, approximately 33 skiers need to go to bring the price per ticket to $16.00.