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.

Question

25-04-2018
Mathematics

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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.

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cerverusdante cerverusdante · Answer 1 · 2018-05-04T22:44:12+02:00

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

[tex]10x+5 \geq 200[/tex]

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