AnswersAL-Algebra I with Probability Critical StandardsModeling with Two-Variable Linear Inequalities

Modeling with Two-Variable Linear Inequalities Answers

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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
2
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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
3

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"?

A
4x + 8y < 50
B
4x + 8y ≤ 50
C
4x + 8y > 50
D
4x + 8y ≥ 50
4

When planning for a party, one caterer recommends the amount of meat be 2 pounds fewer than the total number of guests. The customer decides they want at least that amount of meat. Which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?

Question illustration
A
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 2) and (1, 1). Everything to the right of the line is shaded.
Option A
B
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 2) and (1, 1). Everything to the left of the line is shaded.
Option B
C
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 2) and (3, negative 1). Everything below and to the right of the line is shaded.
Option C
D
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 2) and (3, negative 1). Everything above and to the left of the line is shaded.
Option D
5

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
C
Option
D
Option
6

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
7

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
8

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
9

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
B
Option
C
Option
D
Option
10

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.

Question illustration
A
5
B
6
C
7
D
10
11

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)? Note that the graphs have miles for the independent variable on the x-axis, and the y-axis is a unit of time dependent on the number of miles.

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
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?

A
x + y < 8
B
x + y > 8
C
x + y ≤ 8
D
x + y ≥ 8
13

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

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