Question

Rochelle works part-time at the college museum, which pays her at a rate of $10 per hour. She also makes small bracelets that she sells for $5 a piece. She needs to earn at least $200 a week to cover her expenses.

Answer 1

Answer:

D

(5,15) lies outside the solution region, Rochelle will not be able to cover expences

Step-by-step explanation:

If x represents the number of hours that Rochelle works at the museum, then she will earn $10x. If  y represents the number of bracelets she sells, then she will earn $5y. In total, she will get $(10x+5y). She needs to earn at least $200 a week to cover her expenses, so

10x+5y≥200.

To draw the region that represents the inequality, first draw the line

10x+5y=200.

When x=0, 5y=200 → y=40

When y=0, 10x=200 → x=20

Plot points (0,40) and (20,0) and connect them with solid line (options C and D show needed line).

Now, determine which part you have to choose: since the coordinates of the origin do not satisfy the inequality, the origin does not belong to the region. So option D is correct choice.

If x=5 and y=15, you have that

10·5+5·15=50+75≤200,

the point (5,15) lies outside the region and Rochelle will not be able to cover her expences.

Step-by-step explanation:

Answer 2

We know for our problem that Rachel makes $10 per hour. Since represent the number of hours that she works, will be the total amount that she will make for working hours. We also know that she sells bracelets for $5 each. Since represents the number of of bracelets that she sells, will be her total revenue for selling bracelets. We also know that she needs to earn at least $200 a week to cover her expenses, so the sum of and must be equal or greater than 200:



We can conclude that the graphs that shows the inequality that represents this situation, with its solution region shaded is: