The ice skating rink charges an hourly fee for skating and $3 to rent skates for the day. Gillian rented skates and skated for 3 hours and was charged $21. Which equation represents the cost, c(x), of ice skating as a function of x, the number of hours of skating?

Question

14-06-2016
Mathematics

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The ice skating rink charges an hourly fee for skating and $3 to rent skates for the day. Gillian rented skates and skated for 3 hours and was charged $21. Which equation represents the cost, c(x), of ice skating as a function of x, the number of hours of skating?

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itswhatevaig itswhatevaig · Answer 1 · 2016-06-14T00:13:43+02:00

itswhatevaig itswhatevaig

14-06-2016

c(x) = 6x + 3
shee skated for 3 hrs and was charged $21
c(3) = 6(3) + 3
c(3) = 18 + 3
c(3) = 21
correct....so it is c(x) = 6x + 3

Answer Link

BladeRunner212 BladeRunner212 · Answer 2 · 2019-08-26T16:55:23+02:00

C(x) = 6x + 3 (in USD)

Further explanation

Given:

The fee to rent is $3 for the day.
Gillian rented skates and skated for 3 hours and was charged $21.

Question:

The equation that represents cost, C(x), ice skating as a function of x, the number of hours of skating.

The Process:

We try solving a word problem about the single variable equation.

Step-1: calculate the cost of skates per hour.

Let the rate of using the skating rink be R per hour. We will seek the value of R.

On that day Gillian rented skating for 3 hours and paid $ 21. The equation that will determine this given by:

[tex]\boxed{ \ 3R + 3 = 21 \ }[/tex]

Both sides subtracted by 3.

[tex]\boxed{ \ 3R = 18 \ }[/tex]

We isolate R on the left side. Both sides are divided by 3.

Hence, the fee of skates per hour is [tex]\boxed{R = \$6}[/tex]

Step-2: determine the cost equation for ice skating

Let x as the number of hours of skating.

Recall the fee of skates per hour is $6 and the fee to rent is $3 for the day.

Thus, the equation which represents the cost of ice skating as a function of x, the number of hours of skating, will be given by:

[tex]\boxed{ \ C(x) = 6x + 3 \ }[/tex] (in USD)

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Keywords: the ice skating rink, charges an hourly fee, Gillian rented skates, the equation represents the cost, C(x), a function of x, the number of hours of skating, a word problem, the single variable equation