Solving a Two-Job Earnings Problem
I can help you solve the problem. To answer the question, we will follow these steps:
### Part a:
We need to write an equation with the given information. Maggie has one job that pays $9 per hour and another that pays $11 per hour. We'll use the variable \( x \) to denote the number of hours she works at the $9 per hour job and \( y \) for the number of hours she works at the $11 per hour job.
Given that Maggie earns a total of $297 in one week, the equation based on this information will be:
\[ 9x + 11y = 297 \]
### Part b:
To find the x-intercept, set \( y = 0 \) and solve for \( x \). To find the y-intercept, set \( x = 0 \) and solve for \( y \).
#### X-intercept \( (x, 0) \):
\[ 9x + 11(0) = 297 \]
\[ 9x = 297 \]
\[ x = \frac{297}{9} \]
\[ x = 33 \]
So the x-intercept is \( (33, 0) \).
#### Y-intercept \( (0, y) \):
\[ 9(0) + 11y = 297 \]
\[ 11y = 297 \]
\[ y = \frac{297}{11} \]
\[ y = 27 \]
So the y-intercept is \( (0, 27) \).
Therefore, the x-intercept is 33 and the y-intercept is 27.
