Question - Solving a Two-Job Earnings Problem
Solution:
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.
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