Question

bike rentals at bike shop x it costs $2.75 per hour plus a $3.00 deposit to total cost, c, of renting a bike for n hours at either bike shop can be represent rent the bike for the cost to be less to rent a bike from bike shop x. a. bike shop x c = 2.75n + 3 bike shop z c = 1.75n + 7 b. bike shop x c = 2.75n - 3 bike shop z c = 1.75n - 7 c. bike shop x c = 1.75n + 7 bike shop z c = 2.75n + 3 d. bike shop x c = 1.75n + 3 bike shop z c = 2.75n + 7

Explanation:

Step1: Identify Shop X's cost formula

The problem states Bike Shop X charges $2.75 per hour plus a $3.00 deposit. So its cost equation is $c = 2.75n + 3$. This eliminates options C and D.

Step2: Eliminate invalid cost formulas

Cost cannot be calculated with subtraction of deposit/fees (as in option B, since that would imply negative cost for short rentals, which is impossible). So option B is invalid.

Step3: Verify Shop X is cheaper

For option A, set up the inequality for Shop X cost < Shop Z cost:
$2.75n + 3 < 1.75n + 7$
Subtract $1.75n$ from both sides:
$1.00n + 3 < 7$
Subtract 3 from both sides:
$n < 4$
This means for rental times less than 4 hours, Shop X is cheaper, which fits the problem's requirement.

Answer:

A. Bike Shop X: $c = 2.75n + 3$, Bike Shop Z: $c = 1.75n + 7$