Help please!!

Of all the pairs of consecutive even integers whose sum is greater than 44, find the pair whose sum is the least.

Question

Help please!!

Of all the pairs of consecutive even integers whose sum is greater than 44, find the pair whose sum is the least.

amistre64 · Answer

x + y > 44

let x = 2n
let y=2n+2

2n+2n+2 > 44

solve for n

anonymous · Answer

I dont know how to solve for n

ash2326 · Answer

@Kittykatkat14 Did you understand the explanation given by @amistre64 ?

anonymous · Answer

No, sorry

ash2326 · Answer

you know what are consecutive even integers?

anonymous · Answer

Yes 2,4,6 ... Right?

ash2326 · Answer

Cool, suppose we assume we have one even integer as 2n, what would be the consecutive integer for 2n?

anonymous · Answer

4n?

ash2326 · Answer

If you have 4, what's the next even integer?

anonymous · Answer

2n+2

anonymous · Answer

6

ash2326 · Answer

Yes, so what's the sum of them ?

ash2326 · Answer

sum of 2n and 2n+2

anonymous · Answer

Sum of what?

ash2326 · Answer

2n+2n+2
this is the sum of consecutive integers, isn't it?

anonymous · Answer

Yes

ash2326 · Answer

Now we have the condition, that the sum of consecutive integers should be greater than 44. How would you write that in an equation form?
particularly an inequality

anonymous · Answer

I was looking for least

ash2326 · Answer

Yeah, but first we'll write equation for all greater than 44
$$2n+2n+2>44$$
Is that correct?

anonymous · Answer

Oh okay, yes

shubhamsrg · Answer

Sum of 2 consecutive even integers is greater than 44, but the sum should be least.
We are obviously looking for a+b =46 where a and b are consecutive even integers.

ash2326 · Answer

so we have
$$4n+2>44$$
Yes @shubhamsrg has given us a nice hint
so we have now
4n+2=46
Did you understand ?

anonymous · Answer

Yes i understand, so it would be 22 and 24?

ash2326 · Answer

yes :)

anonymous · Answer

How bout least?

anonymous · Answer

a+b=42?

ash2326 · Answer

This is the least sum, which is greater than 44

anonymous · Answer

Greater or less than?

ash2326 · Answer

Of all the pairs with sum greater than 44, find the ones with the least sum?
so we know it has to be greater than 44 but least
46 satisfies both conditions

ash2326 · Answer

It's like find the least integer greater than 10?
it has to be 11

anonymous · Answer

Is it less than 46 or 44? Nothing says that less than 46?

ash2326 · Answer

greater than 44, but least
what's the next even integer after 44?