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Two shops rent canoes for a rental fee plus a fee per hour. The table shows the total cost (in dollars) for x hours at Shop B is represented by the equation y=4x+6. Which shop charges less per hour? How many hours must a canoe be rented for the total costs to be the same? (PLEASE SHOW WORK)

Two shops rent canoes for a rental fee plus a fee per hour The table shows the total cost in dollars for x hours at Shop B is represented by the equation y4x6 W class=

Respuesta :

Using linear functions, it is found that:

  • Shop A charges less per hour.
  • The canoe must be rented for 3 hours for the costs to be the same.

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 Shop A, we have a linear function that:

  • Has a rate of change of $3, hence m = 3.
  • The intercept is b = y(0) = 12 - 3 = 9.

Hence the functions are given by:

  • A(x) = 3x + 9.
  • B(x) = 4x + 6.

Due to the lower slope, shop A charges less per hour. The costs will be the same when:

A(x) = B(x)

3x + 9 = 4x + 6

x = 3.

The canoe must be rented for 3 hours for the costs to be the same.

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

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