A taxi service charges a flat fee of $1.25 and $0.75 per mile. If Henri has $14.00, which of the following shows the number of miles he can afford to ride in the taxi?
A. [tex]m \leq 17[/tex]
B. [tex]m \geq 17[/tex]
C. [tex]m \leq 20.3[/tex]
D. [tex]m \geq 20.3[/tex]
Answer (2)
Henri can afford to ride at most 17 miles in the taxi based on the fare structure given. The final inequality we derived was m ≤ 17 . Therefore, the correct answer is option A: m ≤ 17 .
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Set up the inequality representing the total cost of the taxi ride: 1.25 + 0.75 m ≤ 14.00 .
Subtract 1.25 from both sides: 0.75 m ≤ 12.75 .
Divide both sides by 0.75 : m ≤ 17 .
Henri can afford to ride at most 17 miles: m ≤ 17 .
Explanation
Understanding the Problem Let's break down this problem. Henri has a certain amount of money, and he wants to use it to pay for a taxi ride. The taxi charges a flat fee plus a per-mile charge. We need to figure out how many miles he can travel without exceeding his budget.
Setting up the Inequality Let m be the number of miles Henri can afford to ride. The total cost of the ride can be expressed as the flat fee plus the cost per mile times the number of miles: 1.25 + 0.75 m . Since Henri has $14.00 , the total cost must be less than or equal to $14.00 . This gives us the inequality: 1.25 + 0.75 m ≤ 14.00
Isolating the Variable Term Now, let's solve the inequality for m . First, subtract 1.25 from both sides: 0.75 m ≤ 14.00 − 1.25 0.75 m ≤ 12.75
Solving for m Next, divide both sides by 0.75 to isolate m : m ≤ 0.75 12.75 Now we perform the division: 12.75 ÷ 0.75 = 17 . Therefore, m ≤ 17
Final Answer So, Henri can afford to ride at most 17 miles.
Examples
Imagine you're planning a road trip and need to budget for gas. If you know your car's gas mileage (miles per gallon) and the price of gas per gallon, you can use a similar inequality to determine how far you can travel on a certain amount of money. For example, if you have $50 and gas costs $2.50 per gallon, and your car gets 25 miles per gallon, you can calculate the maximum distance you can drive. This type of problem helps you make informed decisions about your travel plans and manage your budget effectively. The math looks like this:
Let d be the distance you can drive in miles. The amount of gas you can buy is 2.50 50 = 20 gallons. The distance you can drive is 20 gallons × 25 miles/gallon = 500 miles.
So, you can drive 500 miles on $50 .
