As a pizza deliverer, Sarah is paid [tex]$6.25[/tex] per hour and [tex]$0.32[/tex] per mile. If [tex]t[/tex] represents the number of hours Sarah works in a week and [tex]m[/tex] represents the number of miles driven for deliveries that week, which of the following equations represents [tex]P[/tex], Sarah's income for the week (not including tips)?

A. [tex]P = 6.25t + 0.32m[/tex]

B. [tex]P = 0.32t + 6.25m[/tex]

C. [tex]P = 32t + 6.25m[/tex]

D. [tex]P = 6.25t + 32m[/tex]

Certainly! Let's break down the problem step-by-step to determine the correct equation to represent Sarah's income for the week.

1. Identify Sarah's Pay Rates:
- Sarah gets paid \[tex]$6.25 for each hour she works.
- Sarah gets paid \$[/tex]0.32 for each mile she drives for deliveries.

2. Define Variables:
- Let [tex]$ t $[/tex] represent the number of hours Sarah works in a week.
- Let [tex]$ m $[/tex] represent the number of miles Sarah drives for deliveries in a week.

3. Calculate Income Based on Hours Worked:
- If Sarah works for [tex]$ t $[/tex] hours, her income from working these hours is:
[tex]\[
\text{Income from hours} = 6.25 \times t
\][/tex]

4. Calculate Income Based on Miles Driven:
- If Sarah drives [tex]$ m $[/tex] miles for deliveries, her income from driving these miles is:
[tex]\[
\text{Income from miles} = 0.32 \times m
\][/tex]

5. Combine Both Sources of Income:
- Sarah’s total weekly income [tex]$ P $[/tex] is the sum of her income from hours worked and miles driven:
[tex]\[
P = (\text{Income from hours}) + (\text{Income from miles})
\][/tex]

6. Form the Equation:
- Substitute the expressions for each part of the income into the equation:
[tex]\[
P = 6.25t + 0.32m
\][/tex]

Therefore, the equation that represents Sarah's income [tex]$ P $[/tex] for the week, taking into account both her hourly rate and the miles driven, is:

[tex]\[
\boxed{P = 6.25t + 0.32m}
\][/tex]

This corresponds to the option:

A. [tex]$ P = 6.25t + 0.32m $[/tex]