How to calculate value of x in (1875+y):(x+y)=165

Question

I need to solve this equation but every time I get a different result.Ive tried "find out $x$" calculators online but they fail with "error" or "invalid [...]".

The equation is $(1875+y):(x+y)=165$

(I don't know what tags to use for this question)

Answer 1

$\frac{1875+y}{x+y}=165$, so $1875+y=165x+165y$, so $165x=1875-164y$, so $x=\frac{1875-164y}{165}$.

Answer 2

The "$:$" sign is for Ratio, it tells how the first quantity relates to the second quantity in terms of amount/units (both the quantities should be measured in the same unit).

$x:y=2:1$ means $x$ is twice as much as $y$, and the ration $x:y$ is calculated by $\frac{x}{y}$, so in this example $\frac{x}{y}=\frac{2}{1}$, we omit $1$, because it does not affect the right hand side.

Your example is $(1875+y):(x+y)=165:1$, which means we are considering $165$ units of $(1875+y)$ per unit of $(x+y)$.