Question

Which of the following situations could be reasonably modeled by the equation $5.00x + $0.50y = $25? Select all that apply.

a) Buying 5 items priced at $5 each and 10 items priced at $0.50 each.
b) Renting a room for $25 with an initial deposit of $5 and a daily charge of $0.50.
c) Earning $25 from selling 5 items for $5 each and 10 items for $0.50 each.
d) Paying for a monthly subscription that costs $5 for the base service and an additional $0.50 per premium feature.

Answer 1

The equation $5.00x + $0.50y = $25 could reasonably model option b and d, which involve renting a room with a deposit and a daily charge or paying for a subscription service with a base rate and additional premium features.

Step-by-step explanation:

The equation $5.00x + $0.50y = $25 can be used to model a situation where x represents the number of items or services at a rate of $5.00, and y represents the number of items or services at a rate of $0.50. It's a linear equation, and it helps us understand relationships in various financial situations.

1. Option a: Buying 5 items at $5 each and 10 items at $0.50 each would total $25 + $5, which is not equal to $25. Hence, it cannot be represented by the equation.
2. Option b: Renting a room for $25 that includes an initial deposit and a daily charge can indeed be modeled by this equation, where x represents the number of days rented and y would be the number of initial deposits, though it is unusual for a deposit to be considered a variable as it is typically a one-time fee.
3. Option c: Earning $25 by selling 5 items for $5 each and 10 items for $0.50 each sums to $25 + $5, which exceeds $25. This scenario cannot be represented by the equation.
4. Option d: The monthly subscription with a base service and per premium feature charge fits the model perfectly when x represents the base service, and y represents the number of premium features.