Question

The number of boys varies directly as the number of girls and inversely as the number of teachers. When there are 24 boys and 16 girls, there are 2 teachers. How many girls are there when there are 72 boys and 6 teachers?

Answer 1

24:16:2
72:x:6

you see that the numbers have increased by three times so by following that, you increase the number of girls too.

therefore, x=16*3=48

Answer 2

Yes, that's what I thought. But my mothers answer book says it's a three digit number. I however, can no make that work in any way.

Answer 3

Hmm... In that case... Oh wells...

Answer 4

Starting numbers. Boys = 24. Girls = 16. Teachers = 2.
Ending with Boys = 72. Girls = x. Teachers = 6.

The number of teachers triples. Since teachers and boys are inversely proportional, the number of boys goes down to a third. 24/3 = 8.

However the number of boys is 72, not 8. That means girls have come in and raised the number. So 8 times the number of times the number of girls increased (sorry for language), which we will call X, is 72.

That is, 8x = 72, x = 9.

So thats how many times the number of girls increased. 16 times 9 is 144. Thats the final number of girls.

Answer 5

Perhaps my wording on the middle part made it confusing?

Answer 6

No, I get it now. I managed to work it out myself before I saw this, but this helps me quite a lot. Thanks!