# Cost prices, selling prices

I have a question in maths regarding GST, cost prices and selling prices.

(GST is government services tax, the amount added on to an amount for the government, so it is basically tax)

There are two questions I don't quite understand.

1) If the cost price of an item is $300 (excluding GST) find the selling price and the GST. (GST percentage is 15%) 2) The selling price of an item is$600 (including GST). Find the cost price and the GST.

I already know the formula "Cost Price+GST=Selling price' however I don't quite understand this formula.

For example, with question two I was told to do 600/1.15, but why do you do this.

If you could show me how to use this formula with these two questions it would be great.

Thank a lot.

Let $C$ denote the cost price; let $G$ denote the government services tax (GST); let $S$ denote the selling price. The GST is $15\%$ of the cost price. Thus, $$G = 0.15C \tag{1}$$ The selling price is the sum of the cost price and the GST, so \begin{align*} S & = C + G \tag{2}\\ & = C + 0.15C\\ & = (1 + 0.15)C\\ & = 1.15C \tag{3} \end{align*}
If the cost price of an item is $\$ 300$, find the selling price and GST. To find the GST, substitute$\$300$ for $C$ in equation 1. To find the selling price, substitute $\$ 300$for$C$in equation 3. If the selling price of an item is$\$600$, find the cost price and the GST.
Dividing both sides of the equation 2 by $1.15$ yields $$\frac{S}{1.15} = C \tag{4}$$ To find the cost price, substitute $\$ 600$for$S$in equation 4. If we solve equation 2 for G, we obtain $$G = S - C \tag{5}$$ To find the GST, substitute$\$600$ for $S$ and the cost price you just calculated for $C$ in equation 5.
By definition, $$\frac {GST}{cost\ price}=15\%$$ so,$$GST=0.15\ cost\ price$$ Your formula "cost price + GST = 1.15 cost price = selling price"