Modeling with Two-Variable Linear Inequalities: Quiz

Dominick is training for a race. He spends 0.75 hours running each time he runs and 1.5 hours swimming each time he swims. This week, he spent more than 6 hours training for the race. Which graph represents his possible training times this week?

A. Dashed line shaded above 4 y and 8 x

A hook in an office storage closet can hold no more than 6 pounds. An order of jumbo paperclips weighs 2 pounds and an order of packing tape weighs 3 pounds. If x is the number of orders of paperclips and y is the number of orders of packing tape, which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?

A. Graph one (line going through 2y and 3x)

At lunch, Kira eats either a burrito containing 490 milligrams of sodium or a peanut butter sandwich containing 700 milligrams of sodium. Her doctor told her to reduce her sodium to no more than 4,000 milligrams per week. Which inequality represents x, the number of microwave burritos, and y, the number of peanut butter sandwiches, she can eat each week?

B. 490x + 700y ≤ 4000

Turkey sandwiches cost $2.50 and veggie wraps cost $3.50 at a snack stand. Ben has sold no more than $30 worth of turkey sandwiches and veggie wraps in the first hour of business. Let x represent the number of turkey sandwiches and y represent the number of veggie wraps. The inequality 2.50x+3.50y30 represents the food sales in the first hour. If Ben has sold 4 veggie wraps, what is the maximum value of turkey sandwiches Ben could have sold?

B. 6

Lola bought x pencils that cost $0.25 each and y erasers that cost $0.50. She spent less than $3. Which graph represents Lola's purchase?

C. dashed line 6 and 12

Last year, Jess saw x dramas and y comedies at the movie theater. If she went to the theater no more than 8 times, which inequality best represents the number of movies she saw?

C. x + y ≤ 8

On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points. Lorenzo needs at least 50 points on the final to earn a "B" in the class. Which inequality represents x, the number of correct multiple-choice questions, and y, the number of correct word problems, he needs to earn a "B"?

D. 4x + 8y ≥ 50

It takes Dimitri 9 minutes to make a simple bracelet and 20 minutes to make a deluxe bracelet. He has been making bracelets for longer than 120 minutes. If x represents the number of simple bracelets that he has made and y represents the number of deluxe bracelets he has made, the inequality 9x + 20y > 120 represents the scenario. Which is a possible combination of bracelets that Dimitri may have made?

D. 7 simple bracelets and 3 deluxe bracelets

A manufacturing machine has two processes. One of them is repeated 4 times and the second only once. The entire cycle can take no longer than 3 minutes. Which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?

D. Solid line shaded to the left

One company estimates same-day delivery as more than three less than half the total number of miles. Which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?

D. dashed line shaded above the line -3 and past 5