# Math Help - Break even question

1. ## Break even question

A student a ski trip over March Break determined that his break even point(zero profit) accours if he can sell ski packages to 12 students. he also knows that when he sells 16 ski packages he will maxmize his profit at $2000. a. Asume that relation for his profit is quadratic. b.Determine the algebric expression in standard form that models his profit. c. what is his profit if he sells 18 packages? d. how many student were on trip if his profit is$875?

2. Originally Posted by usm_67
A student a ski trip over March Break determined that his break even point(zero profit) accours if he can sell ski packages to 12 students. he also knows that when he sells 16 ski packages he will maxmize his profit at 2000.
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Hello,

Originally Posted by usm_67
a. Asume that relation for his profit is quadratic.
Let be x = number of students (keep in mind that this x must be a natural number because 1.5 students are quite a funny sight)
Let be p(x) = profit with respect to the number of students.
Then $p(x)=ax^2+bx+c$ is the quadratic equation you're looking for.
Originally Posted by usm_67
b.Determine the algebric expression in standard form that models his profit.
If he sells 0 (zero) packages to 0 (zero) students his profit will be zero (0). So the c of the quadratic equation becomes zero (0):
$p(x)=ax^2+bx$
Now plug in the values you know. You'll get 2 linear equations:
0 = a*144+b*12
2000=a*256+b*16
Solve for a and b and you'll get: a = 31.25 and b = -375

Originally Posted by usm_67
c. what is his profit if he sells 18 packages?
Plug in 18 for x:
$p(18)=31.25\cdot (18)^2-375 \cdot 18=3375$

Originally Posted by usm_67
d. how many student were on trip if his profit is \$875?
Plug in 875 for p(x):

$875=31.25\cdot x^2-375 \cdot x$ This is a quadratic equation in x. Solve for x and you'll get:
x = 14 or x = -2.

(The (-2) students are the missing ones, which will appear in July when the snow has melted away)

Greetings

EB