# Thread: very hard inversely proportional

1. ## 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?????

2. 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: $\displaystyle y = \frac{k}{x}$

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

$\displaystyle y = \frac{k}{120} = \frac{1800}{120} = \frac{180}{12} = \frac{60}{4} = 15$

-----------------------------------------

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

3. 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?

4. 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 $\displaystyle \frac{36}{30} \times 30$ or you can use the equation:

$\displaystyle x = \frac{1800}{50}$

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