there is a sales tax of $22 on an item that costs $272 before tax. the sales tax on a second item is $19.25…

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 $t_1 = 22$ and the pre - tax cost $c_1=272$. So, $r=\frac{t_1}{c_1}=\frac{22}{272}=\frac{11}{136}$.

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 $t_2 = 19.25$, and the tax - rate $r$ is the same for both items. Since $r=\frac{t_2}{c_2}$, we can solve for $c_2$. Rearranging the formula gives $c_2=\frac{t_2}{r}$. Substitute $t_2 = 19.25$ and $r=\frac{11}{136}$ into the formula: $c_2=19.25\div\frac{11}{136}=19.25\times\frac{136}{11}=\frac{19.25\times136}{11}=\frac{\frac{77}{4}\times136}{11}=\frac{77\times34}{11}=7\times34 = 238$.

Answer:

$238$