there is a sales tax of $6 on an item that costs $64 before tax. the sales tax on a second item is $8.25…

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 $t_1 = 6$ and the pre - tax cost $c_1=64$. So, $r=\frac{t_1}{c_1}=\frac{6}{64}=\frac{3}{32}$.

Step2: Find 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 $t_2 = 8.25$, and the tax - rate $r=\frac{3}{32}$. Since $t_2 = r\times c_2$, we can solve for $c_2$ by $c_2=\frac{t_2}{r}$. Substitute $t_2 = 8.25=\frac{33}{4}$ and $r=\frac{3}{32}$ into the formula: $c_2=\frac{\frac{33}{4}}{\frac{3}{32}}=\frac{33}{4}\times\frac{32}{3}$. $c_2 = 88$.

Answer:

$88$