# Algebra

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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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