Select the correct answer.

Julissa is printing out copies for a work training. It takes 4 minutes to print a color copy, and it takes 2 minutes to print a grayscale copy. She needs to print no fewer than 8 copies within 25 minutes.

Which system of inequalities represents the number of color copies, [tex]$x$[/tex], and grayscale copies, [tex]$y$[/tex], that Julissa can print to meet her goal?

A. [tex]$2 x+4 y \leq 25$[/tex] [tex]$x+y \geq 8$[/tex]
B. [tex]$4 x+2 y \geq 25$[/tex] [tex]$x+y \geq 8$[/tex]
C. [tex]$4 x+2 y \leq 25$[/tex] [tex]$x+y \leq 8$[/tex]
D. [tex]$4 x+2 y \leq 25$[/tex] [tex]$x+y \geq 8$[/tex]

Question

Select the correct answer. 
 
Julissa is printing out copies for a work training. It takes 4 minutes to print a color copy, and it takes 2 minutes to print a grayscale copy. She needs to print no fewer than 8 copies within 25 minutes. 
 
Which system of inequalities represents the number of color copies, [tex]$x$[/tex], and grayscale copies, [tex]$y$[/tex], that Julissa can print to meet her goal? 
 
A. [tex]$2 x+4 y \leq 25$[/tex] [tex]$x+y \geq 8$[/tex] 
B. [tex]$4 x+2 y \geq 25$[/tex] [tex]$x+y \geq 8$[/tex] 
C. [tex]$4 x+2 y \leq 25$[/tex] [tex]$x+y \leq 8$[/tex] 
D. [tex]$4 x+2 y \leq 25$[/tex] [tex]$x+y \geq 8$[/tex]

GinnyAnswer · Answer

Define x as the number of color copies and y as the number of grayscale copies. 
 Express the time constraint: 4 x + 2 y ≤ 25 . 
 Express the copy number constraint: x + y ≥ 8 . 
 The correct system of inequalities is: 4 x + 2 y ≤ 25 and x + y ≥ 8 , which corresponds to option D. 
 
 Explanation 
 
 Define variables Let x be the number of color copies and y be the number of grayscale copies. 
 
 Time constraint The time it takes to print x color copies is 4 x minutes, and the time it takes to print y grayscale copies is 2 y minutes. The total time to print the copies must be no more than 25 minutes, so we have the inequality: 4 x + 2 y ≤ 25 
 
 Number of copies constraint The total number of copies must be no fewer than 8, so we have the inequality: x + y ≥ 8 
 
 Final system of inequalities Therefore, the system of inequalities that represents the given constraints is: 4 x + 2 y ≤ 25 x + y ≥ 8 This corresponds to option D.

Examples 
 Suppose you're baking cookies for a bake sale. You need to make at least 24 cookies, and you have a limited amount of chocolate chips and dough. Each chocolate chip cookie requires 15 chocolate chips and 2 oz of dough, while each sugar cookie needs no chocolate chips and 1 oz of dough. If you have 360 chocolate chips and 32 oz of dough, setting up a system of inequalities helps you determine the possible combinations of chocolate chip and sugar cookies you can make while meeting all the constraints. This ensures you meet the minimum cookie requirement and don't exceed your available resources.

Answer (1)

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