"A student with two summer jobs earns $10 per hours at a cafe and $8 per hour at a market. The student would like to earn at least $800 per month."
a. write and graph an inequality to represent the situation. Include clear labels on the graph.
b. The student work at the market for 60 hours per month and can work at most 90 hours per month. Can the student earn at least $800 each month?
What inequality represents the number of hours that the student can work each month? graph.
What inequality represents the amount that the student can earn each month? graph.
Suppose she works c hours at the cafe, and m hours at the market.
To earn at least $800, we need
10c + 8m >= 800
60 hours at the market means $480
at most 90 hours per month means at most 30 hours at the cafe, for $300
If you have trouble with the graphs, google graphing inequalities for examples. Or, heck, study your text...
a. Let x represent the number of hours worked at the cafe and y represent the number of hours worked at the market. The inequality representing the situation is:
10x + 8y ≥ 800
To graph this inequality, we can rewrite it in slope-intercept form:
8y ≥ -10x + 800
y ≥ (-10/8)x + 100
We can now graph the line y = (-10/8)x + 100 with a solid line to represent the inequality. Make sure to label the axes and indicate which region satisfies the inequality.
b. The student can work at most 90 hours per month, so the inequality representing the number of hours the student can work is:
x + y ≤ 90
To graph this inequality, rewrite it in slope-intercept form:
y ≤ -x + 90
Graph the line y = -x + 90 with a dotted line to represent the inequality.
For the amount that the student can earn each month, the inequality is:
10x + 8y ≥ 800
To graph this inequality, rewrite it in slope-intercept form:
8y ≥ -10x + 800
y ≥ (-10/8)x + 100
Graph the line y = (-10/8)x + 100 with a solid line to represent the inequality.
Make sure to label the axes and indicate which region satisfies the inequality.
a. To write the inequality to represent the situation, let's assume the student works "x" hours at the cafe. Since the student works 60 hours at the market, the total number of hours worked would be 60 + x.
The student earns $10 per hour at the cafe, so the amount earned from the cafe job would be 10x.
The student earns $8 per hour at the market, so the amount earned from the market job would be 8 * 60 = 480.
To earn at least $800 per month in total, the sum of the earnings from both jobs should be greater than or equal to $800:
10x + 480 ≥ 800
To graph the inequality, plot the number of hours on the x-axis and the amount earned on the y-axis. Then, draw a solid line for the equation 10x + 480 = 800.
b. The number of hours that the student can work each month at the market is limited to a maximum of 90 hours. Therefore, the inequality would be:
x ≤ 90.
To graph this inequality, plot the number of hours on the x-axis. Modify the solid line from part (a) to a dotted line and shade the area to the left of the line to represent the values less than or equal to 90.
The inequality representing the amount that the student can earn each month is already given and was derived in part (a): 10x + 480 ≥ 800. Graphically, you can represent this inequality by shading the area above the solid line in part (a), indicating the earnings that are greater than or equal to $800.