Word problem x boys and y girls in a class

In summary: Thank you for your help!In summary, the given conversation discusses the problem of solving for the number of boys and girls in Classes A and B. The solution involves creating equations based on the given information and using them to compare the total number of students in each class. After considering all options, it is determined that the correct system of equations is y-x=4 and 2y-x=13, resulting in x=5 and y=9 for Class A and x=8 and y=4 for Class B.
  • #1
Jaco Viljoen
160
9

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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  • #2
In terms of x and y, how many boys and girls are there in class B?
 
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Likes Jaco Viljoen
  • #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:
  • #4
I am making changes to post 1, or adding my thoughts.
 
  • #5
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.
 
  • #6
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.
 
  • #7
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.
 
  • #8
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.
 
  • #9
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.
 

Related to Word problem x boys and y girls in a class

1. How do you solve a word problem involving boys and girls in a class?

To solve a word problem involving boys and girls in a class, you first need to identify the given information, such as the total number of students, the number of boys, and the number of girls. Then, you can use basic arithmetic operations, such as addition, subtraction, multiplication, and division, to find the solution. It may also be helpful to create a diagram or table to organize the information.

2. What is the formula for solving a word problem with boys and girls in a class?

There is no specific formula for solving a word problem with boys and girls in a class. The approach may vary depending on the given information and the specific question being asked. However, the general steps would involve identifying the given information, setting up equations or expressions, and using basic arithmetic operations to find the solution.

3. Can you give an example of a word problem involving boys and girls in a class?

Sure, here's an example: In a class of 30 students, there are 20 boys and 10 girls. If the teacher randomly chooses 5 students to participate in a project, what is the probability that 2 boys and 3 girls will be selected? To solve this problem, you would need to use the given information to set up equations or expressions and then use basic arithmetic operations to find the probability.

4. What are some tips for solving word problems involving boys and girls in a class?

Some tips for solving word problems involving boys and girls in a class include: carefully reading and understanding the given information, organizing the information in a table or diagram, using clear and concise equations or expressions, and checking your work to ensure the solution makes sense in the context of the problem.

5. How can I improve my problem-solving skills for word problems with boys and girls in a class?

To improve your problem-solving skills for word problems with boys and girls in a class, you can practice solving different types of problems, work on breaking down the problem into smaller, more manageable parts, and seek help from a teacher or tutor if you are struggling. You can also try using different strategies, such as drawing diagrams or making lists, to help you understand and solve the problem.

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