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You want to create a piece of pottery at an art studio. The total cost is the cost of the piece plus an hourly studio fee. The costs at two studios are shown.

The cost in studio A is, Vase: 10 dollars and 49 cents; Studio fee: 8 dollars per hour. Cost in studio B is, Vase: 14 dollars and 99 cents; Studio fee: 6 dollars and 50 cents per hour.

a. After how many hours are the total costs the same at both studios?

You want to create a piece of pottery at an art studio The total cost is the cost of the piece plus an hourly studio fee The costs at two studios are shown The class=

Respuesta :

Using linear functions, it is found that the costs will be the same at both studios after 2.25 hours.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For the functions, we have that:

  • The vase is the intercept.
  • The studio fee is the slope.

Hence the functions are given by:

  • A(x) = 10.49 + 8x.
  • B(x) = 14.99 + 6x.

The costs will be the same when:

A(x) = B(x)

Hence:

10.49 + 8x = 14.99 + 6x.

2x = 4.5.

x = 4.5/2

x = 2.25.

The costs will be the same at both studios after 2.25 hours.

More can be learned about linear functions at https://brainly.com/question/24808124

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