Chapter 1.2, Problem 33P

a. If the tax that you pay when you purchase an item is $12\%$ of the sale price, write an expression that gives the tax on the item with a price p. Write another expression that gives the total price of the item, including tax.

b. What operations are involved in the expressions you wrote?

c. Determine the total price, including tax, of an item that costs $75.

d. Explain how the order of operations helped you solve this problem.

To determine

To find: It is being asked to find the expression for the tax on the item with price P and asked to find the total price of the item.

Answer to Problem 33P

Expression of the price of the item with tax is $P+0.12P$

Explanation of Solution

Given information: We are given with when we purchase an item we need to pay tax 12% on sales price. And the variable is given for the price of the item as P.

Calculation:

The price of an item is “P’’.

The tax is 12%.

Tax on price P is $12\%(p)$$=\frac{12}{100}(p)$$=0.12p$

Expression for tax on item with a price P is $0.12p$

Now, let’s find the expression of the item including tax is Price of the item + tax. Which is $P+0.12P$

Simplify it, it gives $1.12P$ .

To determine

To find: It is being asked to find the operation involved in the expression 1.12p.

Answer to Problem 33P

The operations involved in 1.12p are Addition andMultiplication

Explanation of Solution

Given information: The expression $1.12P$

Explanation:

The expression was found using $P+0.12P$

Here $0.12P$ involves multiplication

But $P+0.12P$ involves addition.

To determine

To find: It is being asked to find tax price of an item if it is purchased for $75.

Answer to Problem 33P

Cost of the item including tax =$84.

Explanation of Solution

Given information:Cost of the item is $75.

Calculation:

Let’s find tax for the price $75 by plug in P as 75 into expression $P+0.12P$ .

So, 75+0.12(75) =75 + 9 =$84

To determine

To find: It is being asked to find order of operation helped.

Answer to Problem 33P

Order of operation used is PEMDAS.

Explanation of Solution

Given information: The expression $0.75+0.12(75)$ .

Here the problem having multiplication and addition operation . So, using PEMDAS rule we did multiplication first 0.12 times 75 then added 75 and answer we got from 0.12(75).