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]
