Question

If a varies jointly as b and c, and a = -10, when b = 12 and c = 2, how do you find a when b = 8 and c = ½?

Answer 1

`a = -5/3 = -1 2/3`

Explanation:

There are two ways to find the answer, finding the constant of proportionality or just setting up a proportion.

Finding the constant of proportionality :

`a = kbc`

Plug in the first set of numbers to find `k`:

`-10 = k * 12 * 2`

`-10 = 24k`

`k = -10/24 = -5/12`

Now use `k` to find `a`:

`a = -5/12 *8/1 *1/2 = -40/24 = -5/3 = -1 2/3`

Using proportions:

`(a_1)/(a_2) = (b_1 c_1)/(b_2 c_2)`

`(-10)/(a_2) = (12*2)/(8/1*1/2)`

`(-10)/(a_2) = 24/4`

Use the cross product `a/b = c/d`: `" "a*d = b*c`

`-10 * 4 = 24*a_2`

`-40 = 24 * a_2`

`a_2 = -40/24 = -5/3 = -1 2/3`