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March 30, 2017

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three numbers are such that the second is the difference of three times the first and 6 while the third is the sum of 2 and 2/3 the second. The sum of the three numbers is 172. Find the largest number.

  • Algebra - ,

    n1= first number

    n2 = second number

    n3 = third number



    n2 = 3 n1 - 6


    n3 = 2 + ( 2 / 3 ) n2

    n3 = 2 + ( 2 / 3 ) * ( 3 n1 - 6 )

    n3 = 2 + ( 2 / 3 ) * 3 n1 - ( 2 / 3 ) * 6

    n3 = 2 + 2 n1 - 4

    n3 = 2 n1 - 2


    n1 + n2 + n3 = 172

    n1 + 3 n1 - 6 + 2 n1 - 2 = 172

    6 n1 - 8 = 172 add 8 to both sides

    6 n1 - 8 + 8 = 172 + 8

    6 n1 = 180 Divide both sides by 6

    n1 = 180 / 6 = 30


    n2 = 3 n1 - 6

    n2 = 3 * 30 - 6 = 90 - 6 = 84


    n3 = 2 n1 - 2

    n3 = 2 * 30 - 2 = 60 - 2 = 58


    The largest number = n2 = 84

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