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

A. 106

Explanation:

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

`f(x) =(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((5)/(6)x+5)`

`=5((5)/(6)x+5)+6`

`=(25)/(6)x+25+6` ( From equation (2) )

`=(25)/(6)x+31`

For 18 shirts, i.e. x = 18

The selling price would be,

`g(f(18))=(25)/(6)* 18+31=75+31=106`

Option 'A' is correct.