Bridget purchased 3 pairs of shoes online. The total bill of $126.81 included a $7.50 shipping charge and 6% tax on the total purchase. If the shoes that Bridget purchased were all priced the same, how much did each pair of shoes cost?
A. $37.52
B. $39.77
C. $42.42
D. $112.56
Answer (1)
Subtract the shipping cost from the total bill: 126.81 − 7.50 = 119.31 .
Determine the cost of the shoes before tax: 1.06 x = 119.31 , so x = 1.06 119.31 ≈ 112.56 .
Divide the total cost of the shoes by 3 to find the cost per pair: 3 112.56 ≈ 37.52 .
The cost of each pair of shoes is $37.52 .
Explanation
Problem Analysis Let's analyze the problem. Bridget bought 3 pairs of shoes, and we need to find the cost of each pair. The total bill includes shipping and tax. We'll start by subtracting the shipping cost from the total bill, then account for the tax to find the price of the shoes before tax. Finally, we'll divide by 3 to find the cost per pair.
Defining the variable Let x be the total cost of the 3 pairs of shoes before tax and shipping. The total bill is given as $126.81 , which includes a $7.50 shipping charge and 6% tax on the total purchase.
Subtracting Shipping Cost First, subtract the shipping cost from the total bill: 126.81 − 7.50 = 119.31 This gives us the total cost of the shoes plus the tax.
Accounting for Tax Now, let's account for the 6% tax. The tax is calculated on the price of the shoes, x . So the tax amount is 0.06 x . The equation representing the cost of the shoes plus tax is: x + 0.06 x = 119.31
Combining Like Terms Combine the terms with x : 1.06 x = 119.31
Calculating Total Cost of Shoes Now, divide both sides by 1.06 to find the value of x : x = 1.06 119.31 = 112.5566037735849 So, the total cost of the 3 pairs of shoes before tax and shipping is approximately $112.56 .
Calculating Cost Per Pair Since the shoes are all priced the same, divide the total cost by 3 to find the cost of each pair: 3 112.5566037735849 = 37.5188679245283
Rounding to Nearest Cent Rounding to the nearest cent, the cost of each pair of shoes is $37.52 .
Final Answer Therefore, the cost of each pair of shoes is $37.52 .
Examples
Imagine you're planning a group outing to an amusement park. You need to calculate the cost per person, but the total bill includes transportation and a group discount. By subtracting the transportation cost and accounting for the discount, you can determine the actual cost of admission per person. This is similar to calculating the cost of the shoes by removing shipping and tax, ensuring everyone pays their fair share. This skill is useful for budgeting and splitting costs in various group activities.
