AMC 10 Weekly Practice Round 2

Complete problem set with solutions and individual problem pages

Problem 5 Medium

Three types of saline solutions with salt concentrations of 20\%, 18\%, and 16\% are mixed in certain proportions to obtain 100\,\text{g} of a solution with a salt concentration of 18.8\%. If the amount of 18\% saline solution is 30\,\text{g} more than that of the 16\% saline solution, how many grams of the 16\% saline solution were used?

  • A.

    6 grams

  • B.

    10 grams

  • C.

    12 grams

  • D.

    15 grams

  • E.

    20 grams

Answer:B

\text{Let the saline solution with } 20\% \text{ concentration be } A,\ 18\% \text{ be } B,\ \text{and } 16\% \text{ be } C.

Let the mass of solution B be x\,\text{g}, then the mass of solution C is (x - 30)\,\text{g}, and the mass of solution A is (130 - 2x)\,\text{g}.

The total salt content equation is: 20\% \times (130 - 2x) + 18\% \times x + 16\% \times (x - 30) = 100 \times 18.8\%

Solving gives:x = 40

Then: \text{Solution } A: 130 - 2x = 130 - 2 \times 40 = 50\,\text{g}

\text{Solution } C: 40 - 30 = 10\,\text{g}

Answer: The masses of the saline solutions with concentrations of 20\%, 18\%, and 16\% are 50\,\text{g}, 40\,\text{g}, and 10\,\text{g}, respectively.

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