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. (A. 106; B. 120; C. 185; D. 196)

Answer 1

Answer:

A. 106

Step-by-step explanation:

Given function that represents the cost of materials to make x shirts,

$f(x) =\frac{5}{6}x+5----(1)$

Also, the function for the selling price of x shirts,

$g(f(x))$

Where, $g(x)=5x+6---(2)$

From equation (1),

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

$=5(\frac{5}{6}x+5)+6$

$=\frac{25}{6}x+25+6$  ( From equation (2) )

$=\frac{25}{6}x+31$

For 18 shirts, i.e. x = 18

The selling price would be,

$g(f(18))=\frac{25}{6}\times 18+31=75+31=106$

Option 'A' is correct.