Maths-

General

Easy

Question

# 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.

Hint:

### 1. Cost of extra hours = number of hours performed × rate per extra hour

2. Total cost = Constant fees + cost of extra hours performed.

## 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.

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