Final answer:
The unknown quantity represented by the variable x is the number of hours bikes are rented. The units of the variable are hours. East Side Bike Rentals is a better deal when the bike is rented for more than 5 hours, as shown by the inequality x > 5.
Step-by-step explanation:
To determine when East Side Bike Rentals is a better deal than West Side Bike Rentals, we need to write an inequality that compares the two rates. Let's use x to represent the number of hours the bike is rented, which is the unknown quantity, and the units are hours.
The total cost for West Side Bike Rentals can be expressed as $5 + $0.80x, and the total cost for East Side Bike Rentals can be expressed as $8 + $0.20x. East Side Bike Rentals is a better deal when its total cost is less than that of West Side Bike Rentals. This gives us the inequality $8 + $0.20x < $5 + $0.80x.
To solve the inequality:
Subtract $0.20x from both sides: $8 < $5 + $0.60x.
Subtract $5 from both sides: $3 < $0.60x.
Divide both sides by $0.60 to find the number of hours when East Side becomes a better deal: x > 5.
So, East Side Bike Rentals is a better deal when the bike is rented for more than 5 hours.
We could have written the inequality using either < or > depending on the context. In this case, we used < to indicate when East Side is cheaper (a better deal). If we wanted to know when West Side is a better deal, we would use >.