If the honda civic costs $15 plus $0.50 per mile driven and the ford focus costs $25 plus $0.25 how many miles must you drive the honda civic so it can be the better option???

To find out when the Honda Civic becomes the better option compared to the Ford Focus, we need to set up an equation where the cost of renting the Honda Civic is less than or equal to the cost of renting the Ford Focus.

Let's denote the number of miles driven as "x."

The total cost for the Honda Civic would be: Cost of Honda Civic = $15 + $0.50 * x

And the total cost for the Ford Focus would be: Cost of Ford Focus = $25 + $0.25 * x

We want to find out when the cost of the Honda is less than or equal to the cost of the Ford: $15 + $0.50 * x <= $25 + $0.25 * x

Now, we can solve the inequality:

Subtract $0.25 * x from both sides: $15 + $0.25 * x <= $25

Subtract $15 from both sides to get the terms with x alone on one side: $0.25 * x <= $10

Finally, divide both sides by $0.25 to solve for x: x <= $10 / $0.25 x <= 40

So, you must drive more than 40 miles for the Honda Civic to become the better option. This is because at exactly 40 miles both options cost the same, which is $35 ($15 base price + $0.50 * 40 miles for the Honda, and $25 base price + $0.25 * 40 miles for the Ford). Any additional mile beyond 40 miles will make the Honda the more economical choice because you increase by $0.50 per mile for the Honda and by $0.25 per mile for the Ford.

Extra: When comparing two options based on a fixed cost plus a variable cost (like the per-mile charge for cars), it's important to understand that the fixed cost is a one-time fee, while the variable cost depends on the quantity (in this case, miles). The Honda Civic has a lower fixed cost but a higher per-mile charge compared to the Ford Focus. The Ford Focus, while having a higher fixed cost, has a lower per-mile charge. The turning point, or the number of miles at which both options cost the same, is critical, as beyond this point, the option with the lower per-mile cost becomes more economical.

Understanding such cost structures can help students make more informed decisions about everyday situations, such as comparing phone plans, energy tariffs, or transportation costs. Developing the ability to analyze and compare different cost options based on their fixed and variable components is a valuable skill in financial literacy.