Taxi Fare Calculations and Inequalities

The video tutorial explains how to calculate the maximum distance one can travel in a taxi with a budget of $31. It starts by defining the cost structure of the taxi ride, with $1.25 for the first mile and $0.85 for each additional mile. The tutorial then formulates an expression for the total cost and solves an inequality to find the maximum number of miles that can be traveled within the budget. The solution reveals that the maximum distance is 36 miles.

What is the initial cost for the first mile of the taxi ride?

• $0.85

• $1.25

• $2.00

• $1.00

How much does each additional mile cost after the first mile?

• $1.25

• $0.85

• $0.75

• $1.00

If the ride is 10 miles, how many miles are charged at $0.85 per mile?

• 10 miles

• 8 miles

• 9 miles

• 1 mile

What is the expression for the total cost of the ride in terms of miles driven (m)?

• 1.25 + 0.85m

• 1.25m + 0.85

• 1.25 + 0.85(m - 1)

• 0.85 + 1.25(m - 1)

What inequality represents the condition for the total cost being within the budget?

• 1.25 + 0.85m > 31

• 1.25 + 0.85(m - 1) ≤ 31

• 0.85m + 1.25 < 31

• 1.25m + 0.85 ≤ 31

What is the result of combining the constant terms in the inequality?

• 0.45

• 0.85

• 1.25

• 0.4

After isolating the m term, what is the simplified inequality?

• m ≥ 30.6

• 0.85m ≤ 30.6

• 0.85m ≥ 30.6

• m ≤ 30.6

What is the maximum number of miles that can be driven with $31?

• 35 miles

• 36 miles

• 37 miles

• 38 miles

What is the final step in solving the inequality for m?

• Divide both sides by 0.85

• Subtract 0.85 from both sides

• Add 0.85 to both sides

• Multiply both sides by 0.85

What is the purpose of subtracting 0.4 from both sides of the inequality?

• To simplify the inequality

• To balance the equation

• To eliminate the m term

• To isolate the constant term