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1. The sum of the ages of Ed and his father is 59 years. If his father's age is 11 years less than four times Ed's age, how old is Ed?

2. Five less than seven times a certain number is 58.Find the number.

3. The sum of 1/2 a certain number and 1/3 of the same number is 30. Find the number.

  • math -

    First, we represent the unknown using variables.
    Let x = Ed's age
    Let 59 - x = father's age (since according to the first statement, the sum of their ages is 59)
    Then we setup the equation. According to the second statement,
    Father's age = 4*(Ed's age) - 11
    In variables,
    59 - x = 4x - 11
    59 + 11 = 4x + x
    70 = 5x
    (5x)/5 = (70)/5
    x = 14 years old [Ed's age]

    Represent the unknown with a variable.
    Let x = number
    Then setup the equation using the given conditions.
    7x - 5 = 58
    Solving for x,
    7x = 58 + 5
    7x = 63
    x = 9

    Represent the unknown with a variable.
    Let x = number
    Setup the equation:
    (1/2)x + (1/3)x = 30
    Solve for x. (Recall how to add fractions too)
    (3/6)x + (2/6)x = 30
    [(5/6)x]*(6/5) = 30*6/5
    x = 36

    Hope this helps~ :)

  • math -

    4. The perimeter of a tgriangle is 44 inches. If one side is 5 inches longer than the smallest side and the largest side is 1 inch less than twice the smallest side, how many inches are there in the smallest side?

  • math -

    Represent the unknowns with a variable.

    Let x = smallest side
    Let x + 5 = larger side (according to the 2nd statement)
    Let 2x - 1 = largest side (according to the 2nd statement)
    Then setup the equation. Recall that the perimeter of a triangle is just the sum of the lengths of its sides:
    x + x + 5 + 2x - 1 = 44

    Now solve for x. Units in inches.

    Hope this helps~ :)

  • math -

    thank you for help

  • math -

    I have two more question, I hope you can help me.

    1. A hotel has 120 rooms. If the number of double room is 8 more than three times the number of single rooms, how many single rooms does the hotel have?

    2. A mechanic earns $5 more per hour than his helper. On a six-hour job the two men earn a total of $114. how much does each earn per hour?

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