Thread: Consecutive Integers

My teacher assigned me to do these problems that we have not even taken notes on or even discussed, I have done the first few and I know that I have done them correctly but the others I don't know how to write them out.

- Find two consecutive odd intergers such that the sum of the smaller and 3 times the larger is 330.
- Find three consecutive integers such that the sum of the largest and 5 times the smallest is -224.
- Find three consecutive even intergers such that the sum of twice the smallest and 4 times the largest is 304.
- Find three consqecutive odd intergers such that the sum of 7 times the smallest and twice the largest is -91.

Here is one of the ones that I did correctly and how I did it.
- Find three consecutive intergers whose sum is 51.

n+(n+1)=75
n+n+1=75
2n+1=75-1
2n=74/2
n=37,38

Originally Posted by iSponges

My teacher assigned me to do these problems that we have not even taken notes on or even discussed, I have done the first few and I know that I have done them correctly but the others I don't know how to write them out.

- Find two consecutive odd intergers such that the sum of the smaller and 3 times the larger is 330.
- Find three consecutive integers such that the sum of the largest and 5 times the smallest is -224.
- Find three consecutive even intergers such that the sum of twice the smallest and 4 times the largest is 304.
- Find three consqecutive odd intergers such that the sum of 7 times the smallest and twice the largest is -91.

Here is one of the ones that I did correctly and how I did it.
- Find three consecutive intergers whose sum is 51.

n+(n+1)=75
n+n+1=75
2n+1=75-1
2n=74/2
n=37,38

The one you have given us is...

"Find 2 consecutive integers that sum to 75".

n+(n+1)=75
2n+1=75
2n+1-1=75-1
2n=74
2n/2=74/2
n=37, n+1=38

For the 2 consecutive odd integers question....
The smaller is n and the larger is n+2
so 3 times the larger is 3(n+2)

Then n+3(n+2)=330
n+3n+6=330
4n+6=330
4n+6-6=330-6
4n=324
4n/4=324/4

n=81, n+2=83

Okay, thanks! Homework is now finished

How about trying the other three examples ?

Originally Posted by iSponges

Find two consecutive odd intergers such that the sum of the smaller and 3 times the larger is 330.

2x-1 + 3(2x+1) = 330 ; just wanna see if you follow that...do you?