Mario has a business selling muffins. Let x be the price of a muffin. Then, the profit P for Mario’s business is given by p(x)=-

Question

sasho

3 months ago

5

Mario has a business selling muffins. Let x be the price of a muffin. Then, the profit P for Mario’s business is given by p(x)=-

100x2+350x-150 Choose the inequality that shows the business will make a positive profit.

Mathematics

2 answers:

tester [12.3K] · Answer 1 · 2026-02-22T20:29:37+03:00

The answer to the first question is:

0 <-100x^2+350x-150

For the second question, "Refer to the factorization indicated below.

0 < –100x^2 + 350x – 150

0 < –50(2x^2 – 7x + 3)

0 < –50(2x – 1)(x – 3)

This gives the price range that allows Mario to set his muffin prices and generate a positive profit.

The result is:

$0.50 < x < $3.00

tester [12.3K] · Answer 2 · 2026-02-22T20:32:28+03:00

To achieve a positive profit p(x)>0, we start with:
$-100 x^{2} +350x-150 \ \textgreater \ 0$

Next, we solve for x:
$-2 x^{2} +7x-3 \ \textgreater \ 0$

The parameters are:
a = -2
b = 7
c = -3

We will apply the quadratic formula:
$x_{1} = \frac{-b+ \sqrt{ b^{2}-4ac } }{2a} \\ \\ x_{2} = \frac{-b- \sqrt{ b^{2}-4ac } }{2a} \\ \\ x_{1} = \frac{-7+ \sqrt{ 49-24 } }{-4} = \frac{-7+5 }{-4} = \frac{-2 }{-4} = \frac{1}{2} \\ \\ x_{2} = \frac{-7- \sqrt{ 49-24 } }{-4} = \frac{-7-5 }{-4} = \frac{-12 }{-4} = 3$

This yields two results—one a fraction, the other a whole number. We focus on the whole number since the muffins sold must be a complete unit. Thus we conclude:
x>3