how do you make equation that represents the situation.

Question

The cost y (in dollars) to rent a kayak is proportional to the number $x$x​ of hours that you rent the kayak. It costs $27 to rent the kayak for 3 hours.

a. Write an equation that represents the situation.

Answer 1

Solution:

Let x be the cost/ hr to rent the kayak , and t be the time number of hrs the kayak is rented for

Notice that x is a rate, and so when you combine xt, you get ($/hr) (hr) = $

If the total cost of renting the kayak is $27 dollars, C = $27 and you rent the Kayak for 3hrs, t= 3 hrs, then you can write C = x t , $27 = x ( 3hrs) , and x = $27/ 3hrs = $9/hr

the general formula is then C = xt , C = ( $9/hr) (3hrs) = $27. The outcome of this cost formula can change as x and t values change. so if one variable is fixed say the cost per hr which is x = 9 $/hr, you can write as

C = 9 t and you can determine the cost for any value of t

Answer 2

Since it costs $27 to rent the kayak for 3 hours, then the cost per hour is 27/3 = $9/hr

So, the cost (y) is represented by:

y = 9x (where "x" is the number of hours)

For instance if you rent the kayak for 1 hour the cost is:

y = 9(1) = $9

If you rent the kayak for 2 hours the cost is:

y = 9(2) = $18

If you rent the kayak for 3 hours the cost is:

y = 9(3) = $27

If you rent the kayak for 4 hours the cost is:

y = 9(4) = $36