Let's solve the problem step by step:

Problem Statement:

Mariam took a taxi with:

• A pick-up fee of $2.90
• A charge of $1.25 per mile
• A total fare of $6.65
  We need to write an equation and solve for $m$, the number of miles.

Step 1: Write the Equation

The total fare combines the pick-up fee and the charge for miles driven. This can be written as:
$2.90 + 1.25m = 6.65$
Here:

• $2.90$ is the pick-up fee.
• $1.25m$ is the cost per mile multiplied by $m$, the number of miles.
• $6.65$ is the total fare.

Step 2: Solve for $m$

We isolate $m$ step by step:

1. Subtract 2.90 from both sides:
   $1.25m = 6.65 - 2.90$ $1.25m = 3.75$

2. Divide both sides by 1.25:
   $m = \frac{3.75}{1.25}$ $m = 3$

Final Answer:

• Equation: $2.90 + 1.25m = 6.65$
• Answer: $m = 3$ (the number of miles)

Let me know if you'd like me to explain any step further!

Related Questions:

1. What would the equation look like if the total fare were $8.15 instead?
2. If the rate per mile was $1.50, how would the equation and solution change?
3. How do you solve similar equations with decimals step by step?
4. What happens if the pick-up fee is $5.00 and the total fare is $10.75?
5. How can you check your solution for accuracy in these equations?

Tip: When solving word problems, always identify fixed costs, variable costs, and the total amount to form the equation.