Modeling with Systems of Linear Inequalities — Quiz

Question 1

Which inequality did Jane write incorrectly, and how could it be corrected?

Revolt · Accepted Answer

Inequality 1 is incorrect; it should be g is less than or equal to 80 .

Question 2

There must be more than 4 campers in a group during free play and the difference between the number of boys, x , and the number of girls, y , can be no more than 5 Which graph represents the system of inequalities for this scenario?

Revolt · Accepted Answer

Image with description On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0 comma 4) and (4 comma 0). Everything to the right of the line is shaded. The second dashed line has a positive slope and goes through (0 comma negative 5) and (5 comma 0). Everything to the left of the line is shaded.; Image with description On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0 comma negative 5) and (2 comma negative 3). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0 comma 4) and (2 comma 2). Everything to the right of the line is shaded.

Question 3

Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than 30 inches of wood to use. Which system of inequalities represents the possible length, l , and the possible width, w , that her frame could have?

Revolt · Accepted Answer

l is less than or equal to 12 2 l plus 2 w is less than 30

Question 4

Frosty Fruit makes and sells fruit smoothies and frozen yogurt. Each fruit smoothie costs $⁢8 , and each frozen yogurt costs $⁢3 The manager of Frosty Fruit aims to sell at least 100 items every day and record more than $⁢500 in daily sales. Create a system of two-variable linear inequalities the manager can use to model the sales goals at Frosty Fruit. Let the variable x represent the number of fruit smoothies sold each day. Let the variable y represent the number of frozen yogurts sold each day. Enter your answer in each box.

Revolt · Accepted Answer

x+y≥100|8x+3y>500

Question 5

A salad is made such that the difference between twice the ounces of greens and the ounces of carrots is at least 3 Also, the sum of the ounces of greens and twice the ounces of carrots is less than 4 Which graph represents the system of equations for this scenario?

Revolt · Accepted Answer

Image with description On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0 comma negative 3) and (2 comma 1). Everything to the right of the line is shaded. The second dashed line has a negative slope and goes through (0 comma 2) and (4 comma 0). Everything below of the line is shaded.

Question 6

A city determines that a planned community must have at least 4 acres of developed and open space, and the difference between the number of developed acres, y , and the number of open acres, x , can be no more than 1 Which graph represents the system of inequalities for this scenario? x plus y is greater than or equal to 4 y minus x is less than or equal to 1

Revolt · Accepted Answer

Image with description On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 1 comma 0) and (0 comma 1). Everything below and to the right of the line is shaded. The second line has a negative slope and goes through (0 comma 4) and (4 comma 0). Everything above and to the right of the line is shaded.

Question 7

One winter day, the outside temperature, y , never dropped below negative 1 degree The inside of a car was always warmer than the temperature outside by at least 4 degrees Which graph of a system of inequalities represents this scenario?

Revolt · Accepted Answer

Image with description On a coordinate plane, 2 straight lines are shown. The first solid line is horizontal to the y-axis at y = negative 1. Everything above the line is shaded. The second solid line has a positive slope and goes through (0 comma negative 4) and (4 comma 0). Everything below and to the right of the line is shaded.

Question 8

A baker makes apple tarts and apple pies each day. Each tart, t , requires 1 apple, and each pie, p , requires 8 apples. The baker receives a shipment of 184 apples every day. If the baker makes no more than 40 tarts per day, which system of inequalities can be used to find the possible number of pies and tarts the baker can make?

Revolt · Accepted Answer

t is less than or equal to 40 8 p plus t is less than or equal to 184

Question 9

Consider this system of inequalities. x plus y is less than or equal to negative 3 y is less than x over 2 Which graph shows the solution for this system?

Revolt · Accepted Answer

Image with description On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 3 comma 0) and (0 comma negative 3). Everything to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 2 comma negative 1) and (0 comma 0). Everything to the right of the line is shaded.

Question 10

An arrangement for one container needs to have at least 4 flowers in it and the total wholesale cost must be less than 12 dollars At wholesale, lilies cost 2 dollars per flower and roses cost 3 dollars per flower. If x is the number of lilies and y is the number of roses, which graph represents the system of inequalities for this scenario?

Revolt · Accepted Answer

Image with description On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through 0 comma 4 and 3 comma 2. Everything to the left of the line is shaded. The second solid line has a negative slope and goes through 4 comma 0 and 2 comma 2. Everything to the right of the line is shaded.; Image with description On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through 0 comma 4 and 3 comma 2. Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through 0 comma 4 and 4 comma 0. Everything to the right of the line is shaded.

Modeling with Systems of Linear Inequalities — Quiz Answers

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