girl/boy problem

[Angel Haroon]

I am stuck with this question. So far I don't know where to begin with it.

 

[pka]

I am stuck with this question. So far I don't know where to begin with it.

Suppose that \(G\) is the number of girls and \(B\) is the number of boys.
Then \(G+B=~?\). Moreover, \(B=\frac{1}{2}G\) Tell us why that is true!
Can you finish?

 

[Dr.Peterson]

One way you could think about this would be to draw a picture. Maybe show two equal strips representing all the boys, and the girls they are with; and another strip of the same length representing the other half of the girls. (This will illustrate exactly what pka is suggesting.)

Since your picture represents all 30 students, how many are in each strip?

 

[Angel Haroon]

I have found a different solution.
Let the number of boys be = x
let the number of girls be = 2x ( since the girls are twice than the boys)

so x+2x=30
3x=30
x=10

so 10 boys.

 

[pka]

I have found a different solution.
Let the number of boys be = x
let the number of girls be = 2x ( since the girls are twice than the boys)

so x+2x=30
3x=30
x=10

so 10 boys.

Perfect

 

[HallsofIvy]

But how is that a "different" solution?

 

[Steven G]

You posted this under arithmetic so it is reasonable to assume that you can't use algebra.

You can do this by trial and error.

25 boys: For each boy to sit next to a girl would mean that there are at least 25 girls. But that violates that there are 30 students in the class.

20 boys: For each boy to sit next to a girl would mean that there are at least 20 girls. But that violates that there are 30 students in the class.

15 boys: So there are 15 girls (so the total is 30). After pairing each boy with a girl there are no girls left over. Half of 15 is not 15.

10 boys: So there are 20 girls. 10 sit next to boys and the remaining 10 do not sit next to boys--they sit next to girls. So exactly half the girls sit next to boys!

5 boys: So 25 girls. 5 of them sit next to boys and the remaining 20 do not sit next to boys. Half of 25 is not 5.