Question

The function for the cost of materials to make a shirt is f(x) = five sixths x + 5, where x is the number of shirts. The function for the selling price of those shirts is g(f(x)), where g(x) = 5x + 6. Find the selling price of 18 shirts

Answer 1

$\bf \begin{cases} f(x)=\cfrac{5}{6}x+5\\\\ g(x)=5x+6 \end{cases}\qquad g(\ f(x)\ )=5[\ f(x)\ ]+6 \\\\\\ f(18)=\cfrac{5}{6}(18)+5\implies f(18)=\cfrac{5\cdot 18}{6}+5\implies f(18)=15+5 \\\\\\ \boxed{f(18)=20}\\\\ -------------------------------\\\\ g(\ f(18)\ )=5[\ f(18)\ ]+6\implies g(\ f(18)\ )=5[\ 20\ ]+6 \\\\\\ g(\ f(18)\ )=106$