Word problem x boys and y girls in a class

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Homework Help Overview

The problem involves a class with x boys and y girls, where the girls outnumber the boys by 4. The class joins another class with a different ratio of boys to girls, leading to a comparison of the two classes' compositions. Participants are exploring systems of equations that can represent the relationships between the numbers of boys and girls in both classes.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss various systems of equations to represent the relationships between boys and girls in both classes. There are attempts to derive expressions for the number of boys and girls in Class B based on the information provided about Class A. Some participants express confusion about certain equations and their validity.

Discussion Status

There is ongoing exploration of different options for the systems of equations, with some participants leaning towards specific options while questioning others. A few participants have made progress in understanding the relationships and have begun substituting values into the equations.

Contextual Notes

Participants note constraints such as the requirement that the number of girls cannot be less than 5 based on the problem's conditions. There is also mention of potential typos and the need for clarity in the equations being discussed.

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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.
 
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In terms of x and y, how many boys and girls are there in class B?
 
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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:
I am making changes to post 1, or adding my thoughts.
 
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.
 
Mark44 said:
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.
 
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.
 
Jaco Viljoen said:

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