9
algebra

If 0.1x+0.05(200x)150.1x + 0.05(200 - x) \geq 15, what is the solution?

A

x100x \geq 100

B

x100x \leq 100

C

x50x \geq 50

D

x50x \leq 50

Correct Answer: A

Choice A is the correct answer. This models mixture problems (e.g., interest rates, concentrations).

  1. Distribute: 0.1x+100.05x150.1x + 10 - 0.05x \geq 15
  2. Combine: 0.05x+10150.05x + 10 \geq 15
  3. Subtract 10: 0.05x50.05x \geq 5
  4. Divide by 0.05: x100x \geq 100

?�� Strategic Tip:5÷0.05=500÷5=1005 \div 0.05 = 500 \div 5 = 100.

Choice B is incorrect because it reverses the inequality direction. Choice C is incorrect because it might result from dividing 5 by 0.1. Choice D is incorrect because it combines wrong value and wrong direction.