AnswersAPSB 2025 Math Essentials-ALPGraphing Two-Variable Linear Inequalities

Modeling with Two-Variable Linear Inequalities Answers

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3

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?

Question illustration
A
Option
B
Option
C
Option
D
Option
6

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
8

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
11

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
12

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?

A
490x + 700y < 4000
B
490x + 700y ≤ 4000
C
490x + 700y > 4000
D
490x + 700y ≥ 4000
13

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
14

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?

Question illustration
A
Option
B
Option
C
Option
D
Option
15

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
16

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
17

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
18

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
19

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
20

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

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