QuestionFind the hours for which total costs are equal for two kayak shops: A: \$2 + \$7h, B: \$5 + \$6h.

Studdy Solution

STEP 1

Assumptions1. Shop A has a rental fee of $and an hourly fee of$ 7. Shop B has a rental fee of $5 and an hourly fee of$ 63. We want to find the number of hours for which the total costs at both shops are the same

STEP 2

Let's denote the number of hours for which the kayak is rented as $h$ . The total cost at Shop A for $h$ hours can be calculated by adding the rental fee to the product of the hourly fee and the number of hours.
$Cost_{A} = Rental\, fee_{A} + Hourly\, fee_{A} \\times h$

STEP 3

Substitute the given values for the rental fee and hourly fee at Shop A into the formula.
$Cost_{A} = \$2 + \$7 \\times h$

STEP 4

Similarly, the total cost at Shop B for $h$ hours can be calculated by adding the rental fee to the product of the hourly fee and the number of hours.
$Cost_{B} = Rental\, fee_{B} + Hourly\, fee_{B} \\times h$

STEP 5

Substitute the given values for the rental fee and hourly fee at Shop B into the formula.
$Cost_{B} = \$5 + \$ \\times h$

STEP 6

We want to find the number of hours for which the total costs at both shops are the same. This means that we can set the total cost at Shop A equal to the total cost at Shop B and solve for $h$ .
$Cost_{A} = Cost_{B}$

STEP 7

Substitute the formulas for $Cost_{A}$ and $Cost_{B}$ into the equation.
$\$2 + \$7 \\times h = \$5 + \$6 \\times h$

STEP 8

To solve for $h$ , first simplify the equation by subtracting \$6h from both sides.
$\$2 + h = \$5$

STEP 9

Then, subtract \ $2 from both sides to isolate$ h$.
$h = \$5 - \$2$

STEP 10

Calculate the value of $h$ .
$h = \$3$ So, the total costs are the same when a kayak is rented for3 hours.

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