Mega Mart collects sales tax equals to 1/16 of the retail price. Is the amount of tax collected proportional to the cost of an item before tax is added
Yes.
To determine if the amount of tax collected by Mega Mart is proportional to the cost of an item before tax is added, we need to check if the tax collected is a fixed fraction or percentage of the retail price.
Let's denote the retail price of an item as "x." According to the information given, Mega Mart collects sales tax equal to 1/16 of the retail price.
The amount of tax collected can be calculated as (1/16) * x.
Now, we need to determine if this tax amount is always a fixed fraction or percentage of the retail price, regardless of the value of x.
To do this, we can compare different values of x and see if the ratio of tax amount to the retail price remains constant.
Let's take two different retail prices: x1 and x2.
For x1, the tax collected would be (1/16) * x1.
For x2, the tax collected would be (1/16) * x2.
Now, let's calculate the ratios of tax collected to the retail price for both cases:
For x1: Tax collected / Retail price = ( (1/16) * x1 ) / x1 = 1/16
For x2: Tax collected / Retail price = ( (1/16) * x2 ) / x2 = 1/16
The tax collected as a fraction of the retail price is the same (1/16) for both cases. This means that regardless of the retail price, the amount of tax collected is a fixed fraction or percentage (1/16) of the retail price before tax is added.
Hence, we can conclude that the amount of tax collected by Mega Mart is indeed proportional to the cost of an item before tax is added.