word problem

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I'm embarrassed to admit this but this one has me stumped (it's from my son's math book). Can anyone figure it out?

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

Oh wait... is the answer 675?

Its a trick question isn't it? The number of children is irrelavent to what it asks.


In that case...

the answer would be:

2500 - 1200 = 1300
(people) - (men) = (women)

1300 women

Last edited by Scintillate on 21 Oct 2006, 10:20 am, edited 1 time in total.

800

you sure?

The middle sentence seems to just be totally irrelavent to whether they're male or female, therefore not part of the equation...

I am bad at math but...
if there are 500 hundred kids then 4x tht amount is 2000.....2000 minus 800 is 1200

I think krex is right.

But is there any way to get that number without just guessing a # for the children?

the point I'm getting at, is the question doesn't have any relavence to children at all, it simply says women, which can be of any age can't they?

I swear it, look at the wording of the question, the only factors are:

men

women

and

adults = 4x children

also you have 2500 people

and you're given the number of men but not women, or children.



so it seems to me, "men" and "women" encompass the children too, which means, the number of women, must be the number of people minus the number of men, they are the only two factors given.

If the question asked something about the children I think the answer would be along your lines, but I think the middle sentence is just shoved in there, to confuse.

in other words the middle part of the whole thing isn't needed in the answer at all..

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

becomes

2500 people took part in a cross country race. If there were 1200 men, how many women were there?

hmmn..
men and women can be children too! or am I wrong there?

If men and women are separate from children, then 800 women.

excuse me posting again but just thought I'd add this:

I looked up the definitions of men and women, and you're right, it applies to adult humans.

Let a = the number of adults, m = the number of men, w = the number of women, c = the number of children, and t = the total number of people taking part in the race.

The total number of people taking part in the race, t, is 2500. So t = c + m + w.

The number of adults is 4 times c (4*c), so a = 4c.


1.) Replace the variables with the numbers you already know into the equation t = c + m + w and you get...

2500 = c + 1200 + w

If m + w (or 1200 + w), a, is equal to 4c, then you can also say the opposite, that c is equal to 1/4a (or 1/4(1200 + w)).

2.) Substitute 1/4a in the place of c to get...

2500 = 1/4(1200 + w) + 1200 + w

3.) Use the distributive property of multiplication to get...

2500 = 300 + w/4 + 1200 + w

4.) Subtract to get...

1000 = w/4 + w

5.) Multiply both sides by 4 to get...

4000 = w + 4w

6.) Add to get...

4000 = 5w

7.) Divide to get the number of women who took part in the cross country race.

Is it just me or is that kind of hard for 4th grade?

Yeah they do not make things clear in the question and since this is 4th grade and not 7-8 grade
the answer has to be 2500 -1200 = 1300

Hmm I never learned about variables until I was in the 7th grade, and that was pretty standard for students of that level.

I would assume that the terms "men" and "women" apply to adults, which they do by definition. Therefore

If "x" is the number of children in the race, then 4x is the number of adults and

4x + x = 2500

5 x = 2500

x= 500 (the number of children in the race) and

4x = 2000 (the number of adults)

and 2000 - 1200 = 800 (the number of women). Right? Seems pretty straightforward and OK for fourth grade.