AnswersMathematics IModeling with Two-Variable Linear Inequalities

Modeling with Two-Variable Linear Inequalities — Quiz Answers

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1
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Lola bought x pencils that cost 0 point 25 each and y erasers that cost 0 point 50 dollars She spent less than 3 dollars Which graph represents Lola’s purchase?

A
Image with description A graph titled "Lola's Purchase" shows number of pencils on the x-axis, from 0 to 20, and number of erasers on the y-axis, from 0 to 5. A dashed straight line has a negative slope and goes through 0 comma 3 and 12 comma 0. Everything to the left of the line is shaded.
B
Image with description A graph titled "Lola's Purchase" shows number of pencils on the x-axis, from 0 to 20, and number of erasers on the y-axis, from 0 to 10. A dashed straight line has a negative slope and goes through 0 comma 6 and 12 comma 0. Everything to the left of the line is shaded.
C
Image with description A graph titled "Lola's Purchase" shows number of pencils on the x-axis, from 0 to 20, and number of erasers on the y-axis, from 0 to 10. A solid straight line has a negative slope and goes through 0 comma 6 and 12 comma 0. Everything to the left of the line is shaded.
D
Image with description A graph titled "Lola's Purchase" shows number of pencils on the x-axis, from 0 to 20, and number of erasers on the y-axis, from 0 to 5. A solid straight line has a negative slope and goes through 0 comma 3 and 12 comma 0. Everything to the left of the line is shaded.
2
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A grocery bag contains x apples, each weighing 1 third 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?

A
Image with description A graph titled Grocery Bag Contents shows number of apples on the x-axis, from 0 to 18, and Pounds of Grapes on the y-axis, from 0 to 10. A dashed straight line has a negative slope and goes through 0 comma 5 and 15 comma 0. Everything below and to the left of the line is shaded.
B
Image with description A graph titled Grocery Bag Contents shows number of apples on the x-axis, from 0 to 18, and Pounds of Grapes on the y-axis, from 0 to 10. A dashed straight line has a negative slope and goes through 0 comma 5 and 15 comma 0. Everything above the line is shaded.
C
Image with description A graph titled Grocery Bag Contents shows number of apples on the x-axis, from 0 to 10, and Pounds of Grapes on the y-axis, from 0 to 18. A dashed straight line has a negative slope and goes through 0 comma 15 and 5 comma 0. Everything to the left of the line is shaded.
D
Image with description A graph titled Grocery Bag Contents shows number of apples on the x-axis, from 0 to 10, and Pounds of Grapes on the y-axis, from 0 to 18. A dashed straight line has a negative slope and goes through 0 comma 15 and 5 comma 0. Everything to the right of the line is shaded.
3

Dominick is training for a race. He spends 0 point 75 hours running each time he runs and 1 point 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
Image with description A graph titled "Dominick's Training" shows number of runs on the x-axis, from 0 to 10, and number of swims on the y-axis, from 0 to 5. A dashed straight line with a negative slope goes through (0, 4) and (8, 0). Everything to the left of the line is shaded.
B
Image with description A graph titled "Dominick's Training" shows number of runs on the x-axis, from 0 to 5, and number of swims on the y-axis, from 0 to 10. A dashed straight line with a negative slope goes through (0, 8) and (4, 0). Everything to the right of the line is shaded.
C
Image with description A graph titled "Dominick's Training" shows number of runs on the x-axis, from 0 to 10, and number of swims on the y-axis, from 0 to 5. A dashed straight line with a negative slope goes through (0, 4) and (8, 0). Everything to the right of the line is shaded.
D
Image with description A graph titled "Dominick's Training" shows number of runs on the x-axis, from 0 to 5, and number of swims on the y-axis, from 0 to 10. A dashed straight line with a negative slope goes through (0, 8) and (4, 0). Everything to the left of the line is shaded.
4

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 plus y is less than 45
B
x plus y is greater than or equal to 45
C
x plus y is greater than 45
D
x plus y is less than or equal to 45
7

Dan bought x pounds of potatoes for 0 point 8 5 dollars per pound and y pounds of grapes for 1 point 2 9 dollars per pound. The total cost was less than 5 dollars Which inequality represents his purchase?

A
1 point 2 9 x plus 0 point 8 5 y is greater than 5
B
0 point 8 5 x plus 1 point 2 9 y is less than 5
C
1 point 2 9 x plus 0 point 8 5 y is less than 5
D
0 point 8 5 x plus 1 point 2 9 y is greater than 5
8

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
Image with description On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (3, 0). Everything below and to the left of the line is shaded.
B
Image with description On a coordinate plane, a solid straight line has a negative slope and goes through (0, 3) and (2, 0). Everything to the right of the line is shaded.
C
Image with description On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (3, 0). Everything above and to the right of the line is shaded.
D
Image with description On a coordinate plane, a solid straight line has a negative slope and goes through (0, 3) and (2, 0). Everything to the left of the line is shaded.
10

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 plus y is greater than 8
B
x plus y is less than or equal to 8
C
x plus y is less than 8
D
x plus y is greater than or equal to 8

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