What is five times the smallest of three consecutive integers is seventeen less than twice the sum of the integers. Find the integers

Question

Five times the smallest of three consecutive integers is seventeen less than twice the sum of the integers.  Find the integers

Answer 1

I think a key here is the word Consecutive (one away from each other, increasing).

You could use the classical xyz method or try guessing using a table to help you.

Answer 2

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Answer 3

Hi Devita,

 

The key to this problem is that they are consecutive integers, lets call them x,y,z. So start the set up with:

x+1=y

y+1=z

Then we need to set up the second part of our system of equations:

5x(5 times the smallest)=[when the problem says is, think equals]2(x+y+z)[2 times the sum of the integers]-17 [17 less than 2 times the sum of the integers)

 

Without the commentary, that gives us:

(1)x+1=y --> x=y-1

(2)y+1=z

(3)5x=2(x+y+z)-17

 

The goal is to only have one of our variables present in equation 3. Do this by transforming equations 1 and 2 in your preferred manner. I will isolate x and z so that we can exchange those for an equivalent expression that includes y

 

Plugging those in to equation 3 we get: 5(y-1)= 2(y-1+y+y+1)-17. Just solve for y and then plug your answer into equations 1 and 2 to get your answer.

 

Let me know if you have any more questions,

Brittany