2500 people took part in a cross-country race. The number of adults were 4 times the number of children. If there were 1200 men, how many women were there?

Question

2500 people took part in a cross-country race.  The number of adults were 4 times the number of children.  If there were 1200 men, how many women were there?

lemontoki · Answer

1300 women. Question is phrased a little odd, but I think 1300. Is this a multiple choice or a written response?

cthagard · Answer

This is written response, 4th grade math.

sapphiremoon · Answer

1300 isn't correct. The question mentions there being 4 times more adults than children. If there are 1300 women, then that excludes the possiblility of children. This is fourth grade? Seems like algebra to me...

cthagard · Answer

I have an answer key that says 800 is the correct answer.  I don't know how to figure that with the given information, let alone explain to my son how to get it.

lemontoki · Answer

If there was a number given for the amount of children, then I would just say that you would combine the number of men and children and subtract that from how many people were in attendance total. 
1200(men) + x(children), then subtract that from 2500. That would seem more like a fourth grade level math question.

sapphiremoon · Answer

I can get there algebraically, but no clue how to do it in a way that won't freak out a fourth grader...

lemontoki · Answer

Let me play around real quick and see if i can give show some work to get 800.

lemontoki · Answer

@SapphireMoon thats what i was thinking too. Little bit hard for a fourth grader to understand algebra, but nowadays there doing common core math, which is stupid

sapphiremoon · Answer

I can post my work for this:
$$m + w + c = 2500$$
$$m + w = 4c$$
$$4c + c = 2500$$
$$5c = 2500$$
$$c = 500$$
$$m + w = 4c$$
$$1200 + w = 2000$$
$$w = 800$$
@Cthagard Do you understand this? Maybe you can translate it for your son?

cthagard · Answer

@SapphireMoon, yes I understand this.  Thank you very much.  I was very surprised that this is in elementary math, this early in the school year.  This isn't common core either, it is Singapore math.  Thanks!

lemontoki · Answer

oh geez! well at least @SapphireMoon was able to show some work and help you guys out!

sapphiremoon · Answer

@Cthagard Oh, Singapore! That makes much more sense. That's what I took until 10th grade, I was trying to dumb it down to common-core for you, but Singapore teaches algebra (though not with letters) in first grade, @LemonToki. Glad we could help!