Solve the formula c = 1.06p for p, where c is the cost of an item at Shopping City, including tax, and p is the selling price.
The Correct Answer and Explanation is:
Correct Answer:
To solve the formula c = 1.06p for p, follow these steps: c=1.06pc = 1.06pc=1.06p
Divide both sides of the equation by 1.06: p=c1.06p = \frac{c}{1.06}p=1.06c
Explanation
The formula c = 1.06p shows the relationship between the selling price p of an item and its total cost c at Shopping City, where a 6 percent sales tax is included. The number 1.06 represents the original price (100 percent) plus the 6 percent tax. This equation tells us that when the price of an item is multiplied by 1.06, it gives the final cost the customer pays.
To isolate p and find out the original price before tax, you need to perform algebraic manipulation. The goal is to get p alone on one side of the equation. You start by recognizing that p is being multiplied by 1.06. To reverse this multiplication, you divide both sides of the equation by 1.06.
This gives you: p=c1.06p = \frac{c}{1.06}p=1.06c
This new formula allows you to compute the selling price before tax if you are given the final cost including tax. It is useful in real-life situations like budgeting, returns, or determining pre-tax pricing when planning purchases.
For example, if the total cost of an item is 53 dollars, you can find the pre-tax price by substituting into the formula: p=531.06≈50p = \frac{53}{1.06} \approx 50p=1.0653≈50
So, the original price before tax was about 50 dollars. The extra 3 dollars accounts for the 6 percent tax added to the purchase.
This method works for any percentage-based tax formula where the cost is calculated by multiplying the price by a number slightly greater than 1.
