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SO The sum of four consecutive integers is 16 less than 6 times the first integer. What is the first integer? ​

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Answer : 11

Explanation : The answer before this answer
User Vergel
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4 votes

Answer: 11

Work Shown:

x = first integer

x+1 = second consecutive integer just after x

x+2 = third consecutive integer just after x+1

x+3 = fourth consecutive integer just after x+2

Add up those expressions

(x)+(x+1)+(x+2)+(x+3) = 4x+6

That sum is "16 less than 6 times the first integer", so,

sum = 6*(first) - 16

4x + 6 = 6x - 16

4x-6x = -16-6

-2x = -22

x = -22/(-2)

x = 11 is the first integer

The four consecutive integers are 11, 12, 13, 14.

As a check, the sum is 11+12+13+14 = 50

Then notice how 6x-16 = 6*11-16 = 50 to help confirm we have the correct answer.

User Sam Baker
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