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Word problem x boys and y girls in a class

  1. Apr 22, 2015 #1
    1. The problem statement, all variables and given/known data
    There are x boys and y girls in a class(Class A) The girls outnumber the boys by 4. They join up with another class(Class B) in which there are twice as many boys as girls. Class B has 3 more boys and 5 less girls than class A.
    Which one of the following systems of equations can be used to solve for x and y?

    2. Relevant equations
    1.
    y-x=4
    2y-x=8

    2.
    y-x=4
    2x-y=-13

    3.
    y-x=4
    2y-x=13

    4.
    x-y=4
    2x-y=13

    5.
    y-x=4
    x+2y=7

    3. The attempt at a solution
    y-x=4
    y=x+4
    x=y-4
    x-y=-4
    Class B
    (a)boys = x+3
    (b)girls= y-5
    a=2b
    b=b/2
    x=b-1
    x=a+3
    y=b+5
    y=a-1

    Considering the above the answer must be:
    y-x=4
    this means option 2 is not possible.

    Option 1 also doesn't seem to work.
    Option 5 doesn't make sense to me.

    I am leaning towards option 3 or 4

    x+y+a+b=z


    I feel like this should be simple but I am just not getting it.
    Input would be appreciated.

    Thank you everyone.
     
    Last edited by a moderator: Apr 22, 2015
  2. jcsd
  3. Apr 22, 2015 #2

    haruspex

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    In terms of x and y, how many boys and girls are there in class B?
     
  4. Apr 22, 2015 #3
    Hi haruspex,
    Class B
    boys = x+3
    girls= y-5

    Is this a key to the problem?
    y can't be smaller than 5 but this is already so since y-x=4.
     
    Last edited: Apr 22, 2015
  5. Apr 22, 2015 #4
    I am making changes to post 1, or adding my thoughts.
     
  6. Apr 22, 2015 #5

    Mark44

    Staff: Mentor

    OK, I understand. One equation comes from the information about the boys and girls in class A. The other information comes from writing an equation that compares the total number of students in class A with the total students in class B.
     
  7. Apr 22, 2015 #6
    Yes I think so, but I am not getting it.
     
  8. Apr 22, 2015 #7

    Mark44

    Staff: Mentor

    Class A
    x = no. of boys
    y = no. of girls
    There are 4 more girls than boys, so y = x + 4
    This is equivalent to y - x = 4

    Class B
    Boys -- 3 more than in class A
    Girls -- 5 fewer than in class A

    Write expressions for the no of boys in class B and the no. of girls in class B

    What expression represents the total no of students in class A?
    What expression represents the total no. of students in class B?

    Is class B larger than or smaller than class A?
    By how much is class B larger than or smaller than class A?

    Make an equation (by adding a suitable amount to whichever total is smaller) that compares the numbers of students in the two classes.
     
  9. Apr 22, 2015 #8

    Ray Vickson

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  10. Apr 22, 2015 #9
    Ray,
    thanks for pointing it out, that was a typo was supposed to be a/2
     
  11. Apr 22, 2015 #10
    Class A
    x = no. of boys
    y = no. of girls
    There are 4 more girls than boys, so y = x + 4
    This is equivalent to y - x = 4

    Class B
    Boys -- 3 more than in class A
    Girls -- 5 fewer than in class A

    Write expressions for the no of boys in class B and the no. of girls in class B

    What expression represents the total no of students in class A? x+y
    What expression represents the total no. of students in class B? x+y+3-5=B

    Is class B larger than or smaller than class A? smaller
    By how much is class B larger than or smaller than class A? 2 students less.

    Make an equation (by adding a suitable amount to whichever total is smaller) that compares the numbers of students in the two classes.
    Class B
    x+y-2=B
    x+y+2=A
     
    Last edited: Apr 22, 2015
  12. Apr 22, 2015 #11
    I think I have it:
    We Know x=y-4
    I went through all options and substituted the x with y-4

    Number 3 seems to be my winner

    y-4=x we know this, so correct
    2y-x=13
    2y-(y-4)=13
    2y-y+4=13
    y+4=13

    y=9 and therefore x=5

    Class B
    girls = y-5=4
    boys = x+3=8

    Class B has twice as many boys as girls.

    I was trying to over complicate the problem.
     
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