QuestionTwo shops rent kayaks with different fees. Find hours for equal total costs: Shop A: \$2 + \$7h, Shop 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 cost of renting a kayak from either shop will be the same

STEP 2

Let's denote the number of hours for which the kayak is rented as $h$ . The total cost of renting a kayak from Shop A for $h$ hours is the sum of the rental fee and the product of the hourly fee and the number of hours. This can be represented as $Cost_{A} = Rental\, fee_{A} + Hourly\, fee_{A} \times h$

STEP 3

Similarly, the total cost of renting a kayak from Shop B for $h$ hours is the sum of the rental fee and the product of the hourly fee and the number of hours. This can be represented as $Cost_{B} = Rental\, fee_{B} + Hourly\, fee_{B} \times h$

STEP 4

We want to find the number of hours for which the total cost of renting a kayak from either shop will be the same. This means we need to set $Cost_{A}$ equal to $Cost_{B}$ and solve for $h$ .
$Cost_{A} = Cost_{B}$

STEP 5

Substitute the expressions for $Cost_{A}$ and $Cost_{B}$ from2 and3 into the equation from4.
$Rental\, fee_{A} + Hourly\, fee_{A} \times h = Rental\, fee_{B} + Hourly\, fee_{B} \times h$

STEP 6

Substitute the given values for the rental fees and hourly fees into the equation from5.
$\$2 + \$ \times h = \$5 + \$6 \times h$

STEP 7

Rearrange the equation to isolate the terms involving $h$ on one side and the constants on the other side.
$\$7 \times h - \$6 \times h = \$5 - \$2$

STEP 8

implify the equation.
$h = \$3$ So, the kayak must be rented for3 hours for the total costs to be the same at both shops.

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