Duncan is going to purchase some writing instruments at the school store, where mechanical pencils cost $2 and pens cost $3. He can spend up to $14, but not more. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. x = the number of mechanical pencils Duncan will buy y = the number of pens Duncan will buy Choices: (A)3x * 2y ≤ 14 (B)2x + 3y ≤ 14 (C)2x - 3y ≤ 14 (D)3x + 2y ≤ 14

Question

Duncan is going to purchase some writing instruments at the school store, where mechanical pencils cost $2 and pens cost $3. He can spend up to $14, but not more.  Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. x = the number of mechanical pencils Duncan will buy y = the number of pens Duncan will buy     Choices: (A)3x * 2y ≤ 14 (B)2x + 3y ≤ 14 (C)2x - 3y ≤ 14 (D)3x + 2y ≤ 14

Bytelearn · Accepted Answer

Calculate mechanical pencil cost: Determine the cost per mechanical pencil and the number of mechanical pencils Duncan will buy. Mechanical pencils cost $2 each, and the number of mechanical pencils is represented by x. Therefore, the total cost for mechanical pencils is 2x. Calculate pen cost: Determine the cost per pen and the number of pens Duncan will buy. Pens cost $3 each, and the number of pens is represented by y. Therefore, the total cost for pens is 3y. Combine total costs: Combine the costs for mechanical pencils and pens to represent the total amount Duncan will spend. The total cost is the sum of the cost of mechanical pencils and the cost of pens, which is 2x + 3y. Set spending limit: Duncan can spend up to $14 on writing instruments. This means the total cost for mechanical pencils and pens must be less than or equal to $14. The inequality that represents this situation is 2x + 3y ≤ 14.

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