1
algebra

A coffee shop mixes two types of beans. Type A costs $10/kg and Type B costs $20/kg. To make 10 kg of a mixture costing $14/kg, how many kg of Type A are needed?

A

4

B

8

C

6

D

5

Correct Answer: C

Choice Bhoice D is the correct answer.

  1. Define: Type A = xx, Type B = 10−x10 - x.
  2. Equation: 10x+20(10−x)=14(10)10x + 20(10 - x) = 14(10)
  3. Simplify: 10x+200−20x=14010x + 200 - 20x = 140
  4. Combine: −10x+200=140-10x + 200 = 140
  5. Subtract 200: −10x=−60-10x = -60
  6. Divide by -10: x=6x = 6
  7. Verify: 6(10)+4(20)=60+80=1406(10) + 4(20) = 60 + 80 = 140. 140/10=14140/10 = 14 ✓

Choice Bhoice D is incorrect because this is the amount of Type B.

Choice Bhoice C is incorrect because calculation error.

Choice Bhoice C is incorrect because calculation error.

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Linear Functions Set 30