Question

You work at the local pool as a lifeguard and you also work in the snack bar. You earn $15 per hour lifeguarding and $8 per hour working in the snack

Linear equations and graphs
ANSWERED
asked 2021-06-30
You work at the local pool as a lifeguard and you also work in the snack bar. You earn $15 per hour lifeguarding and $8 per hour working in the snack bar. Last week you worked a total of 20 hours and earned $202.
a. Write an equation in standard form for the hours you worked.
b. Write an equation in standard form for the money you earned.
c. Graph both equations on the same coordinate plane.
d. Determine how many hours you worked as a lifeguard and how many hours you worked in the snack bar. Explain your reasoning.

Answers (1)

2021-07-01

a. Let x be the number of hours you work lifeguarding and y be the number of hours you work in the snack bar. The total number of hours you work is then \(x+y\). Since you worked a total of 20 hours, then \(x+y=20\).
b. If you earn $15 per hour lifeguarding, then after x hours you will earn 15x dollars lifeguarding. If you earn $8 per hour working in the snack bar, then after y hours you will earn 8y dollars. The total amount you will earn is then \(15x+8y\) dollars. Since you earned a total of $202, then \(15x+8y=202\).
c. Solving \(x+y=20\) for y gives \(y=-x+20\). This line has a slope of -1 and a y-intercept of 20 so plot a point at 20 on the y-axis and then use the slope of -1 to plot additional points. Only plot points in the first quadrant since x and yy can't be negative. Then connect the points with a line (shown in red).
Solve \(15x+8y=202\ for\ y: 8y=-15x+202\) \(\displaystyle{y}=-{\left(\frac{{15}}{{8}}\right)}{x}+{25.25}\)
This line then has a slope of −158 and a y-intercept of 25.25 so plot a point at 25.25 and use the slope of −158 to plot additional points. Again, only plot points in the first quadrant. Then connect the points with a line (shown in blue):
[Graph]
d. The two lines in the graph intersect at (6,14). You then work 6 hours lifeguarding and 14 hours in the snack bar.

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