Hey guys,

Having a bit of trouble with this question.

Any help would be greatly appreciated.

Cheers.

Can you add four consecutive whole numbers (e.g., 7, 8, 9, 10) to produce a

multiple of 4? Show using algebra and explain your answer well.

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- Mar 10th 2010, 02:35 AMsmpleasehigh school algebra question
Hey guys,

Having a bit of trouble with this question.

Any help would be greatly appreciated.

Cheers.

Can you add four consecutive whole numbers (e.g., 7, 8, 9, 10) to produce a

multiple of 4? Show using algebra and explain your answer well. - Mar 10th 2010, 03:03 AMHallsofIvy
Alright! High school algebra- one I just might be able to do!

The key word here is**consecutive**. Let x be the smallest of the four numbers. Then the other three are x+ 1, x+ 2, and x+ 3. Add x+ (x+1)+ (x+ 2)+ (x+ 3). What do you get? What does x have to be for that to be a multiple of 4? - Mar 10th 2010, 03:33 AMMarNie
but than it isn't solved yet right?

Or I am I wrong - Mar 10th 2010, 03:58 AMMarNie
anyway good set up for the answer, Because it has been a while for me but I like those puzzles.

am I right that if you simplify it to

4x+6=4y

and assume that x and y both have to be whole numbers

You have the answer? - Mar 10th 2010, 04:54 AMsmplease
yeah i thought of the same start..

x + (x+1) +(x+2)+(x+3) = what?

4x + 6 = what? - Mar 10th 2010, 05:01 AMMarNie
4x+6=4y (4y because it has to be multiplied by 4)

now try to simplify this one as well, so you don't have any whole number on the right hand of the equation

x+6/4=y

Still assuming that x and y have to be whole numbers..... - Mar 10th 2010, 05:05 AMsmplease
thanks for that marnie!

makes sense :D - Mar 10th 2010, 07:19 AMHallsofIvy
No, MarNie, that wasn't solved yet. I prefer not to do people's homework for them.

Yes, it reduces to 4x+ 6= 4y which is, as you say, the same as 4y- 4x= 4(y-x)= 6 or y- x= 6/4= 3/2. Since y and x are integers, that is impossible. - Mar 10th 2010, 07:59 AMMarNie
you're right, I sort of got caught up in it.

It has been a while for me