Question

Alex earns $20.00 an hour doing contract work online and $10.00 an hour at his warehouse job. The monthly payment for his truck is $250.00 and his part of the rent is $750. Alex needs to make at least enough to cover these bills each month.

Which of the following graphs represents this situation?


O.
P.

Q.
R.
A.
R
B.
O
C.
P
D.
Q

Answer 1

To determine which graph represents Alex's situation, we need to set up the conditions based on his earnings and bills.

1. **Income:**
- Contract work: $20.00 per hour (let's denote this as \( x \) hours).
- Warehouse job: $10.00 per hour (let's denote this as \( y \) hours).
- Total income per month = \( 20x + 10y \).

2. **Expenses:**
- Monthly truck payment: $250.00
- Rent: $750.00
- Total expenses = $250 + $750 = $1000.00.

3. **Inequality:**
We want Alex's total income to be at least equal to his expenses:
\[
20x + 10y \geq 1000.
\]

4. **Simplifying the Inequality:**
We can simplify this inequality for easier graphing:
\[
2x + y \geq 100.
\]

This is a linear inequality that represents a region above the line \( 2x + y = 100 \) in the coordinate plane.

To identify which graph (from options O, P, Q, R) corresponds to this situation, look for a graph that features:

- A line with a slope of -2 (which would be the line \( y = -2x + 100 \))
- A shaded area above this line to indicate where Alex earns at least $1000 monthly.

Once you analyze the graphical options, the correct graph representing Alex's financial situation will be the one that fulfills these conditions: a line with the correct slope and shading to indicate the amounts Alex needs to earn.

Please inspect the characteristics of each graph provided to match these criteria.