Q:

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.Let x represent the number of hours that Rochelle works at the museum, and let y represent the number of bracelets she sells.One of the graphs below shows the inequality that represents this situation, with its solution region shaded.Answer the following questions.Which graph shows the inequality that represents this situation with the solution region shaded? (GRAPH A, B, C ,D)Will Rochelle be able to cover her weekly expenses is she works for 5 hours and makes 15 bracelets (YES OR NO)? , because the point (5,15) lies (INSIDE OR OUTSIDE) the solution region.

Accepted Solution

A:
Answer:D(5,15) lies outside the solution region, Rochelle will not be able to cover expencesStep-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 line10x+5y=200.When x=0, 5y=200 → y=40When y=0, 10x=200 → x=20Plot 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.