# The lesser of two consecutive even integers is 10 more than one-half the greater. Find the intergers.?

Help. I've been stuck on this for the past 3 or more hours. Can someone show me the answer and how to answer this kind of question step by step plz cause i have more problems like this and im confused

Relevance

smaller integer=n

n-10=(n+2)/2

n-10=1+n/2

n/2=11

n=22

integers are 22 & 24

The first thing you need to do is construct an algebraic equation for this word problem. In this case, we need to set one thing equal to another. We'll take this in parts (the left side and the right side):

"The lesser of two consecutive even integers is 10 more"

This sets up the beginning of the problem. We will have 2 integers, let's call "a" the smaller one and "b" the bigger one. These integers have to be consecutive AND even, so something like 2 and 4 as opposed to 2 and 3 (which is just 2 consecutive integers). We need "the lesser," and we know it's 10 more. To make it the same as the left side of the equation, we need to take 10 away, so the left of our algebraic equation will be

a-10

"than"

This is where we need to set the left side equal to the right side, so we now have

a-10=

"one-half the greater"

From before, we stated that for this problem, "the greater" is b, so we now have

1/2b

Putting it all together

a-10=1/2b

Now that we have our equation, I just plugged in some values until I got the answer. There is a methodical way to do it. First, we know that 1/2b needs to equal an even number, since a is going to be an even number (and subtracting 10 from an integer will still keep the integer even in this case).

Lets try setting b=28. Half of that is 14. So now

a-10=14 or a=24.

That's not consecutive, so we need to try a number a little smaller. Let's try setting b=16. Half of that is 8. So now

a-10=8 or a=18.

These are two consecutive even integers BUT our "lesser" is bigger than our "greater." We need to try a number a little bigger.

Let's try setting b=24. Half of that is 12. So now

a-10=12 or a=22.

a=22

b=24

Ok so if its even intergers, you can call the smaller one 2x and the larger one 2x + 2. It has to be 2x because that will ensure that it is an even number. so

2x = 1/2 (2x+2) +10

2x = x + 1 + 10

x = 11

so 2x = 22 and 2x + 2 = 24

the lesser is 22, the larger is 24.

whenever you have questions like that, thats the best way to do it rather than trial and error. whenever it talks about even intergers, use 2x :-)