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Solve these two problems: 1. A price increased by 40% to 140. What was the original price? 2. A team has 8 members, 3 of whom are managers. What is the probability of selecting a manager?

Mathematics

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Here are the solutions to the problems:

: Price Adjustment

  1. Define the original price and set up the equation.

    Let the original price be PP.
    A 40% increase means the new price is P+0.40P=1.40PP + 0.40P = 1.40P.
    The final price is given as 140 units.

    1.40P=1401.40P = 140
  2. Solve for the original price PP.

    P=1401.40P = \frac{140}{1.40} P=140014P = \frac{1400}{14} P=100P = 100

    The original price was 100 units.

    : Probability

  3. Identify the total number of members and the number of managers.

    Total number of team members = 8
    Number of managers = 3

  4. Calculate the probability of selecting a manager.

    The probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes.

    Probability (Manager)=Number of managersTotal number of members\text{Probability (Manager)} = \frac{\text{Number of managers}}{\text{Total number of members}} Probability (Manager)=38\text{Probability (Manager)} = \frac{3}{8}

    The probability that the selected person is a manager is 38\boxed{\frac{3}{8}}.

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