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Question

Ms. Rodriguez purchased markers to use on her class whiteboard. She bought a total of 16 markers and three times as many blue markers as red markers.

Set up the two equations that can be used to find the number of markers of each color that Ms. Rodriguez purchased.

Let constraint 1 refer to the equation that represents the total number of markers.
Let constraint 2 refer to the equation that describes the ratio of the number of blue markers to red markers.

Only constraint
would be met if Ms. Rodriguez purchased 3 red markers and 9 blue markers.

Only constraint
would be met if Ms. Rodriguez purchased 6 red markers and 10 blue markers.

Answer 1

Let \( r \) represent the number of red markers and \( b \) represent the number of blue markers.

Constraint 1: \( r + b = 16 \) (Total number of markers)

Constraint 2: \( b = 3r \) (Three times as many blue markers as red markers)

Now we can evaluate the scenarios:

1. For 3 red markers and 9 blue markers:

   • \( r = 3 \)
   • \( b = 9 \)

   Checking the constraints:

   • Constraint 1: \( 3 + 9 = 12 \) (Not met)
   • Constraint 2: \( 9 = 3 \times 3 \) (Met)

   Therefore, only Constraint 2 would be met.

2. For 6 red markers and 10 blue markers:

   • \( r = 6 \)
   • \( b = 10 \)

   Checking the constraints:

   • Constraint 1: \( 6 + 10 = 16 \) (Met)
   • Constraint 2: \( 10 = 3 \times 6 \) (Not met)

   Therefore, only Constraint 1 would be met.

Final answers:

• Only constraint 2 would be met if Ms. Rodriguez purchased 3 red markers and 9 blue markers.
• Only constraint 1 would be met if Ms. Rodriguez purchased 6 red markers and 10 blue markers.