Question

Select the correct answer from each drop-down menu. 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. four graphs for inequality titled rochelles weekly income are shown. graph a and graph b both have solid boundary line intersects x-axis at 40 and y-axis at 20. graph c and graph d both have solid boundary line intersects x-axis 20 and y-axis 40. answer the following questions. which graph shows the inequality that represents this situation with the solution region shaded? will rochelle be able to cover her weekly expenses is she works for 5 hours and makes 15 bracelets? , because the point (5,15) lies the solution region.

Answer 1

The width (w) of the city block is 440 yards.This calculation ensures that Bijan runs a total distance of 8 miles, or 7040 yards, by completing 20 laps around a block with a width of 288 yards.

Step-by-step explanation:

To find the width (w) of the city block using the perimeter formula (P = 320 + w + 320 + w\), which simplifies to (P = 640 + 2w), we can utilize the reciprocal of the total distance Bijan runs. Given that Bijan runs a total of 8 miles, which is equivalent to 7040 yards (since 1 mile = 1760 yards), and he completes 20 laps around the block, we get the distance covered in one lap as 352 yards (since 7040 yards ÷ 20 laps = 352 yards per lap).

The formula for the perimeter of the block
`, \(P = 640 + 2w\),` can be rearranged to solve for \(w\). As we know the total distance covered in one lap is 352 yards, we can set up the equation: (352 = 640 + 2w), subtracting 640 from both sides gives (2w = -288), and solving for (w) yields (w = -144). However, width cannot be negative, so we consider the absolute value, making the width \(w\) equal to 144 yards.

The width of the city block, therefore, is 144 yards, but this is only half the width of the block, as the formula accounts for two widths in the perimeter. Hence, the final width \(w\) of the city block is
`\(2 * 144 = 288\)` yards.

This calculation ensures that Bijan runs a total distance of 8 miles, or 7040 yards, by completing 20 laps around a block with a width of 288 yards.

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Answer 2

Graph B shows the inequality that represents this situation with the solution region shaded. Yes, Rochelle will be able to cover her weekly expenses if she works for 5 hours and makes 15 bracelets, because the point (5,15) lies in the solution region.

Explanation:

Graph B has a solid boundary line that intersects the x-axis at 40 and the y-axis at 20. This means that if Rochelle works for 40 hours at the museum, she will earn $400 (40 x $10) and if she sells 20 bracelets, she will earn $100 (20 x $5), making her total weekly income $500. However, since she only needs to earn $200 to cover her expenses, the solution region is shaded to show all the possible combinations of hours worked and bracelets sold that would result in an income of at least $200.

Now, if we plug in the values of x = 5 and y = 15 into the inequality, we get 5(10) + 15(5) ≥ 200, which simplifies to 50 + 75 ≥ 200, or 125 ≥ 200. This means that Rochelle's income from working for 5 hours and selling 15 bracelets is $125, which is more than enough to cover her expenses.

In other words, Rochelle's weekly income can be represented by the equation 10x + 5y ≥ 200, where x is the number of hours worked and y is the number of bracelets sold. The solution region shaded on graph B shows all the possible solutions that would satisfy this inequality and result in an income of at least $200.

Therefore, graph B is the correct answer as it accurately represents the given situation with its solution region shaded. Rochelle will be able to cover her expenses if she works for 5 hours and makes 15 bracelets, as this point lies in the shaded region indicating a solution to the inequality. This also means that there are other combinations of hours worked and bracelets sold within the shaded region that would result in an income of at least $200, giving Rochelle some flexibility in terms of how she can meet her financial needs.