Thread: high 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.

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?

but than it isn't solved yet right?
Or I am I wrong

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?

yeah i thought of the same start..

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

4x + 6 = what?

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.....

thanks for that marnie!
makes sense

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.

you're right, I sort of got caught up in it.
It has been a while for me