Question: User: 3. Taxi Rides
Taxi Company A charges a $5 starting fee plus $2 per mile. Taxi Company B charges a $10 starting fee plus $1 per mile.
Write a system of equations to represent this relationship. Graph the equations and use the graph to determine the number of miles that would cost the same with each company.
Be sure to use let statements to define variables!
1. **State the problem:**
We want to find the number of miles where the cost of Taxi Company A equals the cost of Taxi Company B.
2. **Define variables:**
Let $x$ be the number of miles.
Let $y$ be the total cost of the taxi ride.
3. **Write the equations:**
For Taxi Company A: $y = 5 + 2x$
For Taxi Company B: $y = 10 + 1x$
4. **Set the equations equal to find the break-even point:**
$$5 + 2x = 10 + 1x$$
5. **Solve for $x$:**
$$5 + 2x = 10 + 1x$$
$$2x - 1x = 10 - 5$$
$$x = 5$$
6. **Interpretation:**
At $5$ miles, both companies charge the same amount.
7. **Calculate the cost at $x=5$ miles:**
For Company A: $$y = 5 + 2(5) = 5 + 10 = 15$$
For Company B: $$y = 10 + 1(5) = 10 + 5 = 15$$
Both cost $15$ at $5$ miles.