An artist charges $20 constant fee plus $10 per extra hour he does. Write the linear model and find the charges taken by him if he works for 4 and a half hours.

The correct answer is: Linear model that represents the fees charged by the artist is y = 20 + 10x and the charges taken by him if he works for 4 and a half hours $60.

Step-by-step solution:-
We are given that-
constant fees = $20
Cost of extra hours performed = $10 / hour
Let x be the number of extra hours performed by the artist and y be the total fees charged by him for the entire performance.
Cost of extra hours = Number of extra hours performed × rate per extra hour
∴ Cost of extra hours = x × 10
∴ Cost of extra hours = 10x .................................................................................................. (Equation i)
Now, we know that-
Total fees charged by the artist = y = constant fees + cost of extra hours performed
∴ y = 20 + 10x ........ (From given information & Equation i) ....................... (Equation ii)
Now, we need to find the total fees charged by the artist if he works 4 and a half extra hours.
∴ x = 4
We substitute x = 4 in Equation ii-
y = 20 + 10x
∴ y = 20 + 10 (4)
∴ y = 20 + 40
∴ y = 60
Final Answer:-
∴ Linear model that represents the fees charged by the artist is y = 20 + 10x and the charges taken by him if he works for 4 and a half hours $60.