Question

Suppose a varies jointly with `b` and `c` and inversely with `d` and `a = 400` when `b = 16`, `c=5`, and `d = 2`. What's the equation that models the relationship?

Answer 1

`ad = 10bc`

Explanation:

If `a` varies inversely with `d`
and jointly with `b` and `c`
then
`color(white)("XXX")ad = k * bc` for some constant `k`

Substituting
`color(white)("XXX")a=400`
`color(white)("XXX")d=2`
`color(white)("XXX")b=16` and
`color(white)("XXX")c=5`

`400 xx 2 = k * 16 xx 5`

`rarr 800 = k * 80`

`rarr k=10`