Question 60672This question is from textbook Essential Algebra
: Hi I am having a problem grasping consecutive integers. I do not know how to write out this equation. Any help would be appreciated.
Thanks,
Lee Ann
Problem: Twice the sum of the first and third of three consecutive integers is fifteen less than the second integer. Find the integers.
This question is from textbook Essential Algebra
Found 2 solutions by praseena, uma:
Answer by praseena(37)   (Show Source):
You can put this solution on YOUR website! here we have three consecutive numbers.
so we can take it as (x-1), x and (x +1 )
sum of the first and third term = x - 1 + x + 1
= x+ x -1 + 1
= 2x
now twicw thw sum of first and third term is = 2 * (2x)
= 4x
now it is given that this 4x is 15 less that the second term
==> 4x = x - 15
==> 4x -x = -15 { bringing like terms together )
==> 3X = -15
==> X = -15/3 { dividing both sides by 3 }
x = -5
thus we got the middle term (second term) is -5
so the first term is x-1 = -5-1
= -6
third term is ( x +1 ) = -5 + 1
= -4
so the terms are -6, -5 and -4
Bye!!!!!!!!!
Answer by uma(370) (Show Source):
You can put this solution on YOUR website! Cosecutive integers are numbers which follow each other.
For example: 2, 3, 4, 5...are consecutive.
Similarly 39, 38, 37, 36, 35,.... are consecutive.
It follows that the integers have a difference of 1.
So let us take the 3 consecutive integers as (x-1), x,(x+1)
Twice the sum of the first and the third integers is
2[(x-1) + (x+1)]
This is 15 less than the second integer.
==> 2[(x-1) + (x+1)] = x - 15
==> 2(x-1+x+1) = x - 15
==> 2(2x) = x - 15
==> 4x = x - 15
==> 4x - x = -15
==> 3x = -15
==> 3x/3 = -15/3
==> x = -5
So the first integer is x - 1 = -5 -1
= -6
The second integer = x
= -5
The third integer = x+1
= -5 + 1
= - 4
The three consecutive integers are -6, -5, -4.
Good Luck!!!
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