# The function for the cost of materials to make a shirt is f(x)=5/6x+5 where xis the number of shirts. The function for the selling price of those shirts is g(f (x)), where g(x)=5x+6. How do you find the selling price of 18 shirts?

Oct 27, 2016

THe answer is $g \left(f \left(18\right)\right) = 106$

#### Explanation:

If $f \left(x\right) = \frac{5}{6} x + 5$

and $g \left(x\right) = 5 x + 6$

Then $g \left(f \left(x\right)\right) = g \left(\frac{5}{6} x + 5\right) = 5 \left(\frac{5}{6} x + 5\right) + 6$

simplifying

$g \left(f \left(x\right)\right) = \frac{25}{6} x + 25 + 6 = \frac{25}{6} x + 31$

If $x = 18$

Then $g \left(f \left(18\right)\right) = \frac{25}{6} \cdot 18 + 31 = 25 \cdot 3 + 31 = 75 + 31 = 106$