there is a sales tax of $4 on an item that costs $54 before tax. the sales tax on a second item is $14. how…

there is a sales tax of $4 on an item that costs $54 before tax. the sales tax on a second item is $14. how much does the second item cost before tax?

there is a sales tax of $4 on an item that costs $54 before tax. the sales tax on a second item is $14. how much does the second item cost before tax?

Answer

Explanation:

Step1: Calculate the tax - rate

First, find the tax - rate for the first item. The tax - rate $r$ is calculated by dividing the tax amount by the pre - tax cost. For the first item, the tax amount $t_1 = 4$ and the pre - tax cost $c_1=54$. So, $r=\frac{t_1}{c_1}=\frac{4}{54}=\frac{2}{27}$.

Step2: Calculate the pre - tax cost of the second item

Let the pre - tax cost of the second item be $c_2$. We know that the tax amount for the second item $t_2 = 14$, and the tax - rate $r=\frac{2}{27}$. Since $r=\frac{t_2}{c_2}$, we can solve for $c_2$. Rearranging the formula gives $c_2=\frac{t_2}{r}$. Substitute $t_2 = 14$ and $r=\frac{2}{27}$ into the formula: $c_2=14\div\frac{2}{27}=14\times\frac{27}{2}=189$.

Answer:

$189$