Set 14: Linear Inequalities

Explanation

Answer: A

A bakery makes bread ( $x$ ) and cakes ( $y$ ). It takes 1 hour to make bread and 2 hours to make a cake. They have at most 10 hours available. They want to make at least 2 loaves of bread. Which system models this?

$x + 2y \leq 10$ and $x \geq 2$

✓ Correct

$x + 2y \geq 10$ and $x \geq 2$

$2x + y \leq 10$ and $x \geq 2$

$x + 2y \leq 10$ and $y \geq 2$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Translate constraints into inequalities. 1. Time Constraint: $1x$ (bread) + $2y$ (cake) $\leq 10$ (hours). $\rightarrow x + 2 y \leq 10$ 2. Quantity Constraint: Bread ( $x$ ) at least 2. $\rightarrow x \geq 2$ 3. System: $x + 2 y \leq 10$ and $x \geq 2$ Strategic Tip: Match the coefficients to the correct variables (1 hour for bread, 2 for cake). Choice B is incorrect because $\geq 10$ means they must work more than 10 hours. Choice C is incorrect because it swaps the time coefficients. Choice D is incorrect because it puts the quantity constraint on cakes ( $y$ ) instead of bread.

Key Steps:

•

The correct answer is $x + 2y \leq 10$ and $x \geq 2$

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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Set 14: Linear Inequalities

Detailed Explanation

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