Math Problem

[5357293]

Hi, this is my first post here and I'm not quite sure which forum this belongs in but I'm having trouble with the question below. I've gotten the answer (24 students total) mainly through trial and error but I don't know what the exact working out is. Would appreciate help!

 

[Harry_the_cat]

Start by introducing some variables. For example, let a be the current number of students in Van A and b be the current number of students in Van B. If you want to find the value of the 2 variables, then you need 2 equations.

Consider the first statement:
"If 2 students move from van A to van B, then the two vans would have the same amount of students in each".

In terms of "a", how many students are now in van A? In terms of "b", how many students are now in van B? What does "have the same amount of students in each" tell you about these two expressions? This will give you one equation.

Now consider the second statement and break it down in a similar way to get a second equation.

Can you proceed? Please show us what you have done.

 

[5357293]

Start by introducing some variables. For example, let a be the current number of students in Van A and b be the current number of students in Van B. If you want to find the value of the 2 variables, then you need 2 equations.

Consider the first statement:
"If 2 students move from van A to van B, then the two vans would have the same amount of students in each".

In terms of "a", how many students are now in van A? In terms of "b", how many students are now in van B? What does "have the same amount of students in each" tell you about these two expressions? This will give you one equation.

Now consider the second statement and break it down in a similar way to get a second equation.

Can you proceed? Please show us what you have done.

What I had gotten were these two expressions:

a-2 = b+2
a+2 = 2(b-2)

And from there, I simplified to
a-b = 4
a-2b = -6

I assume it is a simultaneous equation from here? So van A would have 14 and van B would be 10.

Thank you for your response! It really cleared things up for me

 

[Harry_the_cat]

Brilliant!!

 

[HallsofIvy]

What I had gotten were these two expressions:

a-2 = b+2
a+2 = 2(b-2)

And from there, I simplified to
a-b = 4
a-2b = -6

Yes, and subtracting the second equation from the first eliminates a:

a- b- (a- 2b)= (a- a)- (b- 2b)= b= 4-(-6)= 4+ 6= 10
and a- b= a- 10= 4 so a= 4+ 10= 14.
There are 14 children in bus A and 10 children in bus B.

Check:
Transfering two children from bus A to bus B leaves 14- 2= 12 children in bus A and 10+ 2= 12 children in bus B- the same number of children in both buses.

Transfering two children from bus B to bus A leaves 10- 2= 8 children in bus B and 14+ 2= 16 children in bus A- twice as many children in bus A as in bus B.

I assume it is a simultaneous equation from here? So van A would have 14 and van B would be 10.

Thank you for your response! It really cleared things up for me