a The wages from the hours worked at the cafe plus the wages from the hours worked at the market have to be greater than or equal to 800.
B
b Plot the corresponding ordered pair on your graph. Does it fall in the shaded area?
A
aInequality: 10x+8y≥800
Graph:
B
b No, see solution.
Practice makes perfect
a Let the number of hours worked at the cafe be x and the number of hours worked at the market be y. The student makes $ 10 per hour at the cafe and $ 8 per hour at the market. Let's write an expression for the combined wages earned.
10 x+ 8 y
The student wants to earn at least $800 per month. This means that the wages earned need to be greater than or equal to 800. We can write the situation as an inequality.
10 x+ 8 y≥ 800
If we isolate our y-variable we can graph the inequality as though it is a linear function in slope-intercept form and then shade accordingly.
Now we have a slope of - 54 and a y-intercept of 100. We also know that our graph will be a solid line because y is greater than or equal to 100- 54 x. To find which side of the line to shade, we can test a point. Let's try with the point (0,0).
Since (0,0) is not a solution to our inequality, we should shade on the opposite side of the boundary line.
b The student can work a maximum of 90 hours each month, and is working 60 of those hours at the market. The remaining hours would be worked at the cafe.
Hours at the cafe: 90- 60= 30
The student works 30 hours in the cafe. Since on our graph the x-axis is cafe hours and the y-axis is market hours, we have the ordered pair ( 30, 60). Let's plot this point and see where it lies.
Since the point does not lie within the shaded area, it is not a solution to the system of equations. Therefore, 30 hours at the cafe and 60 hours at the market is not going to let the student reach their goal of at least $800.
