Math  /  Algebra

QuestionA taxi service charges $1.50\$ 1.50 plus $0.60\$ 0.60 per mile for a trip to the airport. The total charge is $13.50\$ 13.50.
Which equation can be used to determine the number of miles, mm, to the airport? A) 10+0.6m=13.510+0.6 m=13.5 B) 1.5+10m=13.51.5+10 m=13.5 C) 0.6+1.5m=13.50.6+1.5 m=13.5 D) 1.5+0.6m=13.51.5+0.6 m=13.5

Studdy Solution

STEP 1

What is this asking? How many miles were traveled if a taxi ride costs $1.50\$1.50 initially, plus $0.60\$0.60 per mile, and the total cost was $13.50\$13.50? Watch out! Don't mix up the initial fee and the per-mile cost!

STEP 2

1. Set up the equation
2. Solve for mm

STEP 3

Alright, let's break this down!
We know the **total cost** of the taxi ride is $13.50\$13.50.
This total cost is made up of two parts: a **fixed initial fee** and a **variable cost** that depends on the number of miles.

STEP 4

The initial fee is a flat $\$1.50, no matter how far you go.
The variable cost is $0.60\$0.60 *per* mile.
If we let mm represent the number of miles, the variable cost is 0.60m0.60 \cdot m.

STEP 5

To get the **total cost**, we add the **initial fee** and the **variable cost** together.
This gives us the equation: 1.50+0.60m=13.501.50 + 0.60 \cdot m = 13.50

STEP 6

Our goal is to isolate mm to find the number of miles.
First, let's subtract the initial fee of $1.50\$1.50 from both sides of the equation.
This is like removing the initial cost to focus on the mileage cost: 1.501.50+0.60m=13.501.501.50 - 1.50 + 0.60 \cdot m = 13.50 - 1.50 0.60m=12.000.60 \cdot m = 12.00

STEP 7

Now, we want to find the value of a *single* mile, so we divide both sides of the equation by 0.600.60.
Think of it as dividing the total mileage cost by the cost per mile to find the number of miles: 0.60m0.60=12.000.60\frac{0.60 \cdot m}{0.60} = \frac{12.00}{0.60} m=20m = 20

STEP 8

The equation that can be used to determine the number of miles, mm, to the airport is 1.5+0.6m=13.51.5 + 0.6m = 13.5, which is option D.
Solving for mm, we find that m=20m = 20 miles.

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