Word problem x boys and y girls in a class

[Jaco Viljoen]

Homework Statement

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?

Homework 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

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

Thank you everyone.

 

[haruspex]

In terms of x and y, how many boys and girls are there in class B?

 

[Jaco Viljoen]

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.

 

[Jaco Viljoen]

I am making changes to post 1, or adding my thoughts.

 

[Mark44]

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.

 

[Jaco Viljoen]

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.

Yes I think so, but I am not getting it.

 

[Mark44]

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.

 

[Ray Vickson]

Homework Statement

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?

Homework 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

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

***************************************
Never write something like this (i.e., b = b/2): it makes no sense and is wrong (unless b = 0).

You just need to say x+3 = 2(y-5). That expresses everything correctly. Of course, you still need to expand it out and simplify.

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

Thank you everyone.

 

[Jaco Viljoen]

Ray,
thanks for pointing it out, that was a typo was supposed to be a/2

 

[Jaco Viljoen]

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

 

[Jaco Viljoen]

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.