Find the three numbers

The second of three numbers is one less than the first. The third number is 5 less than twice the second. If the third number exceeds the first number by 12, find the three numbers.

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x = first number
x - 1 = second number {the second is one less than the first}
2(x - 1) - 5 = third number {the third is 5 less than twice the second}

2(x - 1) - 5 = x + 12 {the third number exceeds the first by 12}
2x - 2 - 5 = x + 12 {used distributive property}
2x - 7 = x + 12 {combined like terms}
x = 19 {subtracted x and added 12 to each side}
x - 1 = 18 {substituted 19, in for x, into x - 1}
2(x - 1) - 5 = 31 {substituted 19, in for x, into 2(x - 1) - 5}

the three numbers are 19, 18, and 31

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