AnswersDRHS-GA-Algebra Concepts and Connections AModeling with Two-Variable Linear Inequalities

Modeling with Two-Variable Linear Inequalities Answers

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1
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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.

A
3 simple bracelets and 4 deluxe bracelets
B
0 simple bracelets and 6 deluxe bracelets
C
12 simple bracelets and 0 deluxe bracelets
D
7 simple bracelets and 3 deluxe bracelets
2
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A grocery bag contains x apples, each weighing of a pound, and y pounds of grapes. The total weight of the grocery bag is less than 5 pounds. Which graph represents the possible numbers of apples and pounds of grapes that can be in the bag?

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B
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D
Option
3

Jamaal spent x minutes today practicing his guitar and y minutes today on homework. If the total time he spent on both is 45 minutes or more, which inequality best represents his practice time?

A
x + y < 45
B
x + y > 45
C
x + y ≤ 45
D
x + y ≥ 45
4

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
Option
B
Option
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Option
D
Option
5

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)?

A
On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (1, negative 1). Everything to the right of the line is shaded.
Option A
B
On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (1, negative 1). Everything to the left of the line is shaded.
Option B
C
On a coordinate plane, a solid straight line has a negative slope and goes through (0, 3) and (1, negative 1). Everything to the right of the line is shaded.
Option C
D
On a coordinate plane, a solid straight line has a negative slope and goes through (0, 3) and (1, negative 1). Everything to the left of the line is shaded.
Option D
6

Mr. Ishimoto ordered x new math books and y new workbooks for his class. The total weight of the box of books cannot be more than 50 pounds. If each math book weighs 3.2 pounds and each workbook weighs 0.8 pounds, which inequality represents the maximum number of each type of book that can be shipped in a single box?

A
3.2x + 0.8y < 50
B
3.2x + 0.8y ≤ 50
C
0.8x + 3.2y < 50
D
0.8x + 3.2y ≤ 50
7

Dan bought x pounds of potatoes for $0.85 per pound and y pounds of grapes for $1.29 per pound. The total cost was less than $5. Which inequality represents his purchase?

A
1.29x + 0.85y < 5
B
1.29x + 0.85y > 5
C
0.85x + 1.29y > 5
D
0.85x + 1.29y < 5
8

A shipping box can carry no more than 6 pounds. Each order of jumbo paperclips weighs 2 pounds, and each order of packing tape weighs 3 pounds. If x is the number of paperclip orders and y is the number of packing tape orders, which graph models the combinations that can be shipped together?

A
Option
B
Option
C
Option
D
Option
9

A career-placement test eliminates a profession when a person receives a score of 18 or less. The score is equal to the formula 2x - 3y, where x is the number of positive responses and y is the number of negative responses. Which graph represents the range of test results that would be eliminated under this scenario (all points may not apply to the scenario)?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

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?

A
Option
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Option
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Option
D
Option

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