The function for the cost of materials to make a biscuit is f(x) = four-fifths x + 4, where x is the number of biscuits. The function for the selling price of those biscuits is g(f(x)), where g(x) = 4x + 5. Find the selling price of 15 biscuits.

Question

anonymous · Answer

i got 65

anonymous · Answer

@SolomonZelman

solomonzelman · Answer

$\large\color{blue}{   f(x)=\frac{4}{5}x+4   }$

$\large\color{blue}{   f(x)   }$ is the cost, for the number of biscuits  $\large\color{blue}{   x   }$.

anonymous · Answer

so 
f(15) = 4/5 (15) + 4?

anonymous · Answer

ohh now i think the answer is 69

solomonzelman · Answer

$\large\color{blue}{   f(x)=\frac{4}{5}x+4   }$      function for the price you buy at.

$\large\color{blue}{   g(x)=4x+5   }$      function for the price you sell at.


so whatever the +4 in the f(x), and the +5 in g(x) .. maybe the delivery.. but that is the delivery/service or whatever per any number of bisuits x in both function.

solomonzelman · Answer

both function*s.

solomonzelman · Answer

So the guy who is selling them makes a big profit... not only off each biscuit, but also from the delivery/service or whatever the y-intercepts are in this case.

anonymous · Answer

so do i have to solve fot the f one first then do the g one?

anonymous · Answer

and add them together?

solomonzelman · Answer

selling price of 15 biscuit would just be,
$\large\color{blue}{   g(15)=4(15)+5   }$

because just like for selling x biscuits you get,  the  $\large\color{blue}{  g(x)   }$,  or 4x+5,
so will the selling price be when there are 15 biscuits, saying when x=15.

anonymous · Answer

so g(15) = 65

solomonzelman · Answer

yes.

anonymous · Answer

so i was write in the beginning

solomonzelman · Answer

The profit on the other hand  (for any number of biscuits x)  would be
$\large\color{blue}{   g(x)-f(x)  }$
or,
making my notations,
$\large\color{blue}{   H(x) = }$$\large\color{blue}{   g(x)-f(x)  }$

$\large\color{blue}{   H(x) =(4x+5)-(\frac{4}{5}x +4)}$

$\large\color{blue}{   H(x) =4x+5-\frac{4}{5}x -4}$

$\large\color{blue}{   H(x) =3\frac{1}{5}x+1}$

solomonzelman · Answer

so H(x) is the profit function.

solomonzelman · Answer

yes, and selling price for 15 biscuits is just g(15) as you have successfully found.

anonymous · Answer

thanks this is so hard i'm good at math but i'm only supposed to be taking algebra 1 so taking algebra 2 puts so much pressure and it's so confusing

solomonzelman · Answer

you are doing very good. you seem to comprehend every thing that you are learning.

solomonzelman · Answer

Just concluding that the selling price is g(15), which is 65... so yw.

anonymous · Answer

:) i have more if you got time ?