algebra

A number n is multiplied by 5/8. The product is subtracted by 2/3. The result 7/12, what is n.

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  1. Translate the English into Math, after all Mathematics is a language.
    "A number n is multiplied by 5/8" --- (5/8)n
    "The product is subtracted by 2/3", poorly worded, I will assume
    you mean -----> (5/8)n - 2/3
    "The result 7/12" -----> (5/8)n - 2/3 = 7/12
    multiply each term by 24, the LCD
    15n - 16 = 14

    continue from here

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  2. 5n/8-2/3=7/12
    2.5n/4-2/3=7/12 multiply each side by 12
    2.5*3n-8=7
    7.5n=15
    n=2

  3. 2 / 3 - n ∙ 5 / 8 = 7 / 12

    2 / 3 - 5 n / 8 = 7 / 12

    8 ∙ 2 / 8 ∙ 3 - 3 ∙ 5 n / 3 ∙ 8 = 2 ∙ 7 / 2 ∙ 12

    16 / 24 - 15 n / 24 = 14 / 24

    Subtract 16 / 24 to both sides

    16 / 24 - 15 n / 24 - 16 / 24 = 14 / 24 - 16 / 24

    - 15 n / 24 = - 2 / 24

    Multiply both sides by 24

    - 15 n = - 2

    Divide both sides by - 15

    n = - 2 / - 15

    n = 2 / 15

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