# Fractions: 4656 people; after 4/5 of men, 3/4 of women leave, there are 120 more women than men remaining

#### jerbeck99

##### New member
This is the word problem,
4656 people at a concert. after 4/5 of the men leave, and 3/4 of the women left the concert hall, there were 120 more women than men who remained behind. How many more women than men were there at 1st?

this is the work my son has tried to do. is this anywhere close?

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#### pka

##### Elite Member
I will set it up and then you can decide. I cannot read his writing.
$$\displaystyle w+m=\text{total}$$
$$\displaystyle \frac{1}{4}w=\frac{1}{5}m+120$$

#### ksdhart2

##### Senior Member
Well, I can tell you for sure the answer's wrong, but even if the answer were correct, I'd consider this working highly unsatisfactory. I find your son's handwriting to be legible but I don't understand what any of the workings shown actually mean. For instance, he begins by saying 4656 total = 3725. This is not off to a promising start as it is an obviously false statement - certainly 4656 is not equal to 3725. Presumably this statement means something to your son but it's not at all clear to me what.

Sadly it doesn't get any better from there, either. The number 3492 is written, just "floating" there, apropos of nothing. I haven't the slightest clue how this number, nor the 3725 from the previous step were obtained. Then he concludes there were 1284 men and 811 women left after removing 4/5 of the men and 3/4 of the women?? Past that I honestly have no idea what happens

I have a strong suspicion that your son would benefit from taking things slowly and clearly writing down every single step he takes, even if it's something as simple as 2 + 3 = 5. I've found that when people are just starting out in math, explicitly writing every step both serves as a check to make sure what they're doing makes sense, and serves as a means to better determine where an error might be if a wrong answer is obtained.

#### Dr.Peterson

##### Elite Member
May I ask what methods he has learned? You posted this under prealgebra (which often actually includes an introduction to algebra); but the obvious way to solve it, as pka indicated, is with a system of two equations in two variables; this is not a very basic algebra problem, though with experience it isn't difficult. Was he trying to use algebra? How much has he learned?

There may be a purely arithmetical and logical way to do it, such as one using pictures, though I don't like applying those to such complicated problems, and I can't think of a method along those lines. The work he did appears random, and I can't see any hints of a method he might have been taught. An example of a solved problem he was shown might help to see what he's expected to do.

#### pka

##### Elite Member
This is not off to a promising start as it is an obviously false statement - certainly 4656 is not equal to 3725. Presumably this statement means something to your son but it's not at all clear to me what.???
Sadly it doesn't get any better from there, either. The number 3492 is written, just "floating" there, apropos of nothing. I haven't the slightest clue how this number, nor the 3725 from the previous step were obtained. Then he concludes there were 1284 men and 811 women left after removing 4/5 of the men and 3/4 of the women?? Past that I honestly have no idea what happens
I have a strong suspicion that your son would benefit from taking things slowly and clearly writing down every single step he takes, even if it's something as simple as 2 + 3 = 5. I've found that when people are just starting out in math, explicitly writing every step both serves as a check to make sure what they're doing makes sense, and serves as a means to better determine where an error might be if a wrong answer is obtained.
\displaystyle \begin{align*}w+m&=46566 \\\frac{1}{4}w&=\frac{1}{5}m+120\\w&=\frac{4}{5}m+480\\\\m+\frac{4}{5}m+480&=4656\\9m&=4656-480\\m&=2320 \end{align*} SEE HERE

#### jerbeck99

##### New member
Thanks for your help. These are random word problems the teacher assigns and doesn't help the students w any sort of method. I didnt know where to post this problem.
I appreciate your help. Thank you all!

#### Dr.Peterson

##### Elite Member
I take it that systems of equations are a reasonable expectation of the students in this class, even though it's called pre-algebra? And your son understands this solution?

You haven't stated what they are learning yet, so I don't know whether to look for an alternative method.