Question

How do you solve `10/12=x/18`?

Answer 1

`x = 15`

Explanation:

You an solve this in two ways: proportionality or just rearranging the equation

Rearranging the equation
You can multiply `10/12` by 18 to leave x to one side.
`10/12 * 18 = x`
`x = 15`

Proportionality
You can work out the proportion between 12 and 18, which will be the same for 10 and `x`.
so `18/12 = 1 1/2`
Therefore, if we multiply 10 by `1 1/2` we get the value of `x` which is `15`

Answer 2

`x=15`

Explanation:

Using first principles

Multiply both sides by `color(red)(18)`

`color(green)(10/12color(red)(xx18)" " =" " x/18color(red)(xx18))`

`color(green)(10/12color(red)(xx18)" " =" " x color(red)(xx)(color(red)(18))/18)`

But `18/18=1` so `x xx18/18 =x xx1=x` giving:

`(10xx18)/12=x`

Write as `" "x=(10xx18)/12" "=" "(2xx5xx2xx3xx3)/(3xx4)`

`x=(2xx2)/4xx3/3xx5xx3" " =" " 1xx1xx15`

........................................................................
or if you prefer:

`x= "(cancel(2)^1xx5xxcancel(2)^1xx3xxcancel(3)^1)/(cancel(3)^1xxcancel(4)^1) = 5xx3=15`