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Thread: Just canít work it out after 3 days of trying

  1. #1
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    Just canít work it out after 3 days of trying

    Hi all I have been trying to work this out for 3 days and seem to be missing something and get a different answer no matter what do.

    Please help




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  2. #2
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    Re: Just canít work it out after 3 days of trying

    start with

    $m + 3m + (3m-10) + \dfrac{3m-10}{4} = 65$

    $\dfrac{31}{4}m - \dfrac{50}{4} = 65$

    $31m - 50 = 260$

    $31m = 310$

    $m = 10$

    10 men
    30 women
    20 girls
    5 boys
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  3. #3
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    Re: Just canít work it out after 3 days of trying

    Quote Originally Posted by romsek View Post
    start with

    $m + 3m + (3m-10) + \dfrac{3m-10}{4} = 65$

    $\dfrac{31}{4}m - \dfrac{50}{4} = 65$

    $31m - 50 = 260$

    $31m = 310$

    $m = 10$

    10 men
    30 women
    20 girls
    5 boys
    Thanks Romsek

    I am only new to algebra so please excuse my ignorance but what does $ stand for and the \defrac as this is not terminology I have been taught so far .

    I really appreciate your help


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  4. #4
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    Re: Just canít work it out after 3 days of trying

    That's Latex ($\LaTeX$) the typesetting language used to render mathematical notation on the site. It's not mathematical notation.

    Your error was in trying to remove the denominator from the fraction. You did it wrong, but also it was the wrong thing to do. You should first look to group like terms. In this case you have terms in $m$ and constant terms, so you need to combine all the terms in $m$ into a single term and all the constant terms into a single term.

    Remember that $\frac{3m+10}{4}=\frac{3m}{4} + \frac{10}{4} = \frac34 m + \frac52$.
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  5. #5
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    Re: Just canít work it out after 3 days of trying

    Quote Originally Posted by Archie View Post
    That's Latex ($\LaTeX$) the typesetting language used to render mathematical notation on the site. It's not mathematical notation.

    Your error was in trying to remove the denominator from the fraction. You did it wrong, but also it was the wrong thing to do. You should first look to group like terms. In this case you have terms in $m$ and constant terms, so you need to combine all the terms in $m$ into a single term and all the constant terms into a single term.

    Remember that $\frac{3m+10}{4}=\frac{3m}{4} + \frac{10}{4} = \frac34 m + \frac52$.
    Thanks Archie

    I seem to be getting more confused by the minute.

    I am stuck on romsekís second line as I can see how he got to there.




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    Re: Just canít work it out after 3 days of trying

    Quote Originally Posted by bartman72 View Post
    Thanks Romsek

    I am only new to algebra so please excuse my ignorance but what does $ stand for and the \defrac as this is not terminology I have been taught so far .

    I really appreciate your help


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    I guess your browser isn't rendering the LaTex

    -clipboard01.jpg
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  7. #7
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    Re: Just canít work it out after 3 days of trying

    Quote Originally Posted by romsek View Post
    I guess your browser isn't rendering the LaTex

    Click image for larger version. 

Name:	Clipboard01.jpg 
Views:	7 
Size:	22.4 KB 
ID:	38910
    Hi Romsek

    I am have trouble understanding how you got to the 31m and 50


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  8. #8
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    Re: Just canít work it out after 3 days of trying

    Quote Originally Posted by bartman72 View Post
    Hi Romsek

    I am have trouble understanding how you got to the 31m and 50


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    I multiplied both sides of the equation by 4.
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  9. #9
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    Re: Just canít work it out after 3 days of trying

    There are 4 unknown values, the number of men, m, the number of women, w, the number of boys, b, and the number of girls, g. We are given 4 pieces of information so can form 4 equations to solve for those 4 values.

    "Three times as many women as men are on the tour": w= 3m.
    "There are 10 less girls than the number of women": g= w- 10.
    "The number of boys is a quarter of the number of girls": b= g/4.
    "There are 65 people booked in for the tour": m+ w+ b+ g= 65.

    I would put everything in terms of m: w= 3m, g= w- 10= 3m- 10, b= g/4= (3m- 10)/4= 3m/4- 10/4= 3m/4- 5/2.

    Then m+ w+ b+ g= m+ 3m+ 3m- 10+ 3m/4- 5/2= 65

    (1+ 3+ 3+ 3/4)m= 65+ 10+ 5/2
    (4+ 12+ 12+ 3)m/4= 155/2
    31m= 310 so m= 10.

    Then w= 3m= 30, g= 3m- 10= 20, and b= 3m/4- 5/2= 30/4- 5/2= 15/2- 5/2= 10/2= 5.

    There were 10 men, 30 women, 5 boys, and 20 girls.

    Check:
    "Three times as many women as men are on the tour": yes, 30= 3(10)
    "There are 10 less girls than the number of women": yes, 20= 30- 10.
    "The number of boys is a quarter of the number of girls": yes, 5= 20/4.
    "There are 65 people booked in for the tour": yes, 10+ 30+ 20+ 5= 65.

    (Checking is important! The first time I did this problem, I accidently swapped two numbers and only caught the error after checking.)
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