Thread: very hard inversely proportional

Hi this is my question:
The grant avalible to a section of society was inversely proportional to the number of people needing the grant. When 30 people needed a grant, the received £60 each.

i worked out that K=1800
But:
a) what would the grant have been if 120 people had needed one?
i get stuck on this bit, would i do this to get the answer?
120/30=4 1800 x 4= 7200?????

Originally Posted by andyboy179

Hi this is my question:
The grant avalible to a section of society was inversely proportional to the number of people needing the grant. When 30 people needed a grant, the received £60 each.

i worked out that K=1800
But:
a) what would the grant have been if 120 people had needed one?
i get stuck on this bit, would i do this to get the answer?
120/30=4 1800 x 4= 7200?????

The relationship of inversely proportional variables is:

In this case y is the amount of grant and x the number of people. You found k (and it's correct) so simply sub your value of k in when x = 120




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Another way to think about it is that every time the number of people double the grant will be half of the previous amount.

As 120/30 = 4 then it follows it will be a quarter of the original amount: 60/4 = 15

thanks.
can you help me on this question aswell?
b) if the grant had been £50 each, how many people would have received it?
would i do:
1800/50= 36 people?

Originally Posted by andyboy179

thanks.
can you help me on this question aswell?
b) if the grant had been £50 each, how many people would have received it?
would i do:
1800/50= 36 people?

You can do either or you can use the equation:



Both of these give an answer of 36 so you're correct