Question

R is inversely proportional to A.

R = 12 when A = 1.5
a) Work out the value of Rwhen A= 5.
b) Work out the value of A when R = 9

Answer 1

a.3.6

b. 2

Explanation:

R is inversely proportional to A

Which means R=k/A

Cross multiply

k=RA

Since R=12

A=1.5

So k=12×1.5

=18

a. We are to determine the value for R

So R=k/A

=18/5

=3.6

b.we are to determine the value for A

So R=k/A

A=k/R

=18/9

=2

Answer 2

Here are the answer: a) R = 3.6 and b) A = 2

Explanation:

Given,

R is inversely proportional to A.

R ∝
`(1)/(A)`

so, R =
`(k)/(A)` -------eq 1 where k is any constant

To find the values of a) R when A = 5 and

b) Value of A when R = 9

Now,

Putting R = 12 and A = 1.5 in eq 1 we get,

12 =
`(k)/(1.5)`

or, k = 12×1.5 = 18

From eq 1 we get,

R =
`(18)/(A)` --------- eq 2

Now,

a) Putting A= 5 in eq 2 we get,

R =
`(18)/(5)` = 3.6

b) Putting R = 9 in eq 2 we get

R =
`(18)/(A)`

or, A =
`(18)/(9)` = 2