three times the sum of three consecutive integers is the same as 78 more than 5 times the largest integer . find the integers

Question

these are simple math world problems that are just tripping me up. Im not sure how to get to the end answer because the wording is confusing to me 

Answer 1

Morgan,

 

Consecutive integers are the numbers the follow one right after the next.  7, 8, and 9 are three consecutive integers.  So are 100, 101, and 102.  

 

Ok, so how do we find 3 consecutive integers when we don't know where to start?  I like to use x because it is the common algebra variable.

 

So if my first number is x

my next number is one more than that (x+1) like 8 is one more than 7

the next number is one more than that (x + 1 + 1) or simply (x+2)

 

Now I have three consecutive integers x, (x+1), and (x+2).  See how if x=7 we have 7, 8, and 9?

 

so we need 3 times the sum of three consecutive integers.

 

So first we add up our integers x + (x+1) + (x+2) = 3x + 3

now we need to multiply that by 3   3(3x+3) = 9x + 9

 

That is equal to (the same as) 78 more than 5 times the largest.

 

well (x+2) is the largest integer so 

 

78 + 5(x+2)

78 + 5x + 10

5x +88

 

9x + 9 = 5x + 88

4x = 79

x = 19.75

 

However, 19.75 is not an integer.  Therefore there must be a problem with the problem.  However, once you find your mistake in typing the problem you can use the set up of this one to find your actual answer.

 

Good Luck,