Question

Wes bought some school supplies at an outlet store in Maine, a state that in 2016 had a5.5% sales tax. Including the sales tax, how much did Wes pay for a jacket priced at $49.95and a pair of pants priced at $17.50?(Continuation) A familiar feature of arithmetic is that multiplication distributes overaddition. Written in algebraic code, this property looks like a(b + c) = ab + ac. Because ofthis property, there are two equivalent methods that can be used to compute the answer in#10. Explain, using words and complete sentences.

Answer 1

Wes paid $52.49225 for the jacket and $18.49375 for the pants, with a combined total cost of $70.986, including the 5.5% sales tax in Maine. This was calculated using distributive property.

Jacket Price Calculation:

Original price of the jacket: $49.95

Sales tax rate: 5.5% or 0.055

Applying the formula "Total Cost = (1 + Tax Rate) * Original Price":

Total Cost for Jacket = (1 + 0.055) * $49.95 = 1.055 * $49.95 = $52.49225

Pants Price Calculation:

Original price of the pants: $17.50

Applying the same formula:

Total Cost for Pants = (1 + 0.055) * $17.50 = 1.055 * $17.50 = $18.49375

Total Cost Calculation:

Adding the total costs of the jacket and pants:

Total Cost = Total Cost for Jacket + Total Cost for Pants

Total Cost = $52.49225 + $18.49375 = $70.986

Therefore, Wes paid $70.986 for the jacket and pants, including the 5.5% sales tax in Maine.

We used distributive property. The distributive property allows for a more efficient and consistent way to calculate the total cost with sales tax, whether considering each item separately or their combined total. It simplifies the arithmetic and ensures that both methods produce the same result.

Answer 2

2016 sales tax in Maine: 5.5%

Wes bought (in dollars):

Jacket: $49.95

Pants: $17.50

First method:

The combined price of those two garments:

pants_and_jacket_price = 49.95 + 17.50 = $67.45

Now, we need to apply the sales tax to this:

5.5% of $67.45 = 5.5*67.45/100 = $3.70975

Finally, we add the pants and jacket price and the sales tax:

total = $67.45 + $3.71 = $71.16

Second method:

We apply the taxes sale individually for the jacket and the pants:

Sales tax:

Jacket: 5.5% of $49.95 = $2.74725

Pants: 5.5% of $17.50 = $0.9625

The total sales tax is: $2.74725 + $0.9625 = $3.70975

Now, we add this to the prices of the jacket and the pants:

total = $49.95 + $17.50 + $3.71 = $71.16

We have these two methods because of the distributive property of multiplication. The sales tax calculation is a multiplication of 5.5/100 (this is the 5.5%) times the total price. But the total price is a sum, the sum of the prices of the jacket and the pants. This is:

sales_tax = 5.5*(49.95 + 17.50)/100 = 5.5*49.95/100 + 5.5*17.50/100

Because of the distributive property, we can solve the problem in two ways. The first method is taking the sum of the prices and then calculate the total sales tax. The second method calculates the sales tax of each garment, and then we add these individual sales taxes to obtain the total one.