Question

How do you solve the system of equations `\frac { 18} { n } = \frac { 54} { n + 40}`?

Answer 1

`n=20`

Explanation:

By cross multiplication we get
`18(n+40)=54n`
Note that `3*18=54`
so
`n+40=3n`

`2n=40`
so `n=20`

Answer 2

`n = 20`.

Explanation:

We have,

`color(white)(xxx) 18/n = 54/(n + 40)`

`rArr 1/n = 3/(n + 40)` [Divide both sides by `18`]

`rArr 3n = n + 40` [Cross-multiply]

`rArr 3n - n = canceln + 40 cancel(-n)` [Subtract `n` from both sides]

`rArr 2n = 40`

`rArr n = 20` [Divide both sides by `2`].

And We got our answer. Hope this helps.