AMC 8 Daily Practice Round 8

Complete problem set with solutions and individual problem pages

Problem 10 Medium

A company originally planned to send \frac{1}{8} of its workers to a short-term training program. Later, 2 more people were added, making the ratio of those who actually attended the training to those who did not 1:6. How many people were originally planned to attend the training program?

  • A.

    14

  • B.

    16

  • C.

    30

  • D.

    112

  • E.

    117

Answer:A

Let the total number of employees be x. According to the problem, the equation can be set up as: \left( \frac{1}{8}x + 2 \right) : \left( x - \frac{1}{8}x - 2 \right) = 1 : 6

This proportion can be rewritten as:

\left( x - \frac{1}{8}x - 2 \right) \times 1 = \left( \frac{1}{8}x + 2 \right) \times 6

Solving the equation gives: x = 112

So, the number of people originally planned to attend the training is:

\frac{1}{8} \times 112 = 14

Related Problems
Problem 8 AMC 8 Daily Practice Round 8
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