real world application: percent of change & sales tax
3. iphone 16
original price: $799
sale price: $759.45
a. how much did the price change?
b. what is the percent of change?
c. sales tax is 3.5%, what would the sales tax be on the sale price?
d. what is the total price including tax?

4. nike hoodie
original price: $80
sale price: $54.99
a. how much did the price change?
b. what is the percent of change?
c. sales tax is 6%. what would the sales tax be on the sale price?
d. what is the total price including tax?

Question

real world application: percent of change & sales tax
3. iphone 16
original price: $799
sale price: $759.45
  a. how much did the price change?
  b. what is the percent of change?
  c. sales tax is 3.5%, what would the sales tax be on the sale price?
  d. what is the total price including tax?

4. nike hoodie
original price: $80
sale price: $54.99
  a. how much did the price change?
  b. what is the percent of change?
  c. sales tax is 6%. what would the sales tax be on the sale price?
  d. what is the total price including tax?

Accepted Answer

### 3. iPhone 16
#### A. How much did the price change?
# Explanation:
## Step1: Subtract sale price from original price
To find the price change, we subtract the sale price from the original price. The formula is: $ \text{Price Change} = \text{Original Price} - \text{Sale Price} $

Given:
- Original Price ($ P_{original} $) = $799
- Sale Price ($ P_{sale} $) = $759.45

So, $ \text{Price Change} = 799 - 759.45 $

## Step2: Calculate the result
$ 799 - 759.45 = 39.55 $

# Answer:
The price changed by $39.55.

#### B. What is the percent of change?
# Explanation:
## Step1: Recall the percent change formula
The formula for percent change is: $ \text{Percent Change} = \frac{\text{Price Change}}{\text{Original Price}} \times 100\% $

We already found the price change is $39.55 and the original price is $799.

## Step2: Substitute the values into the formula
$ \text{Percent Change} = \frac{39.55}{799} \times 100\% $

## Step3: Calculate the fraction first
$ \frac{39.55}{799} \approx 0.0495 $

## Step4: Multiply by 100% to get the percentage
$ 0.0495 \times 100\% = 4.95\% $ (approximately)

# Answer:
The percent of change is approximately 4.95%.

#### C. Sales tax is 3.5%. What would the sales tax be on the sale price?
# Explanation:
## Step1: Recall the sales tax formula
The formula for sales tax is: $ \text{Sales Tax} = \text{Sale Price} \times \text{Tax Rate} $

Given:
- Sale Price ($ P_{sale} $) = $759.45
- Tax Rate ($ r $) = 3.5% = 0.035 (in decimal form)

## Step2: Substitute the values into the formula
$ \text{Sales Tax} = 759.45 \times 0.035 $

## Step3: Calculate the result
$ 759.45 \times 0.035 = 26.58075 \approx 26.58 $ (rounded to the nearest cent)

# Answer:
The sales tax on the sale price would be approximately $26.58.

#### D. What is the total price including tax?
# Explanation:
## Step1: Recall the total price formula
The total price including tax is the sum of the sale price and the sales tax. The formula is: $ \text{Total Price} = \text{Sale Price} + \text{Sales Tax} $

We know the sale price is $759.45 and the sales tax (from part C) is approximately $26.58.

## Step2: Substitute the values into the formula
$ \text{Total Price} = 759.45 + 26.58 $

## Step3: Calculate the result
$ 759.45 + 26.58 = 786.03 $

# Answer:
The total price including tax is $786.03.

### 4. Nike hoodie
#### A. How much did the price change?
# Explanation:
## Step1: Subtract sale price from original price
To find the price change, we use the formula: $ \text{Price Change} = \text{Original Price} - \text{Sale Price} $

Given:
- Original Price ($ P_{original} $) = $80
- Sale Price ($ P_{sale} $) = $54.99

So, $ \text{Price Change} = 80 - 54.99 $

## Step2: Calculate the result
$ 80 - 54.99 = 25.01 $

# Answer:
The price changed by $25.01.

#### B. What is the percent of change?
# Explanation:
## Step1: Recall the percent change formula
The formula for percent change is: $ \text{Percent Change} = \frac{\text{Price Change}}{\text{Original Price}} \times 100\% $

We found the price change is $25.01 and the original price is $80.

## Step2: Substitute the values into the formula
$ \text{Percent Change} = \frac{25.01}{80} \times 100\% $

## Step3: Calculate the fraction first
$ \frac{25.01}{80} \approx 0.3126 $

## Step4: Multiply by 100% to get the percentage
$ 0.3126 \times 100\% = 31.26\% $ (approximately)

# Answer:
The percent of change is approximately 31.26%.

#### C. Sales tax is 6%. What would the sales tax be on the sale price?
# Explanation:
## Step1: Recall the sales tax formula
The formula for sales tax is: $ \text{Sales Tax} = \text{Sale Price} \times \text{Tax Rate} $

Given:
- Sale Price ($ P_{sale} $) = $54.99
- Tax Rate ($ r $) = 6% = 0.06 (in decimal form)

## Step2: Substitute the values into the formula
$ \text{Sales Tax} = 54.99 \times 0.06 $

## Step3: Calculate the result
$ 54.99 \times 0.06 = 3.2994 \approx 3.30 $ (rounded to the nearest cent)

# Answer:
The sales tax on the sale price would be approximately $3.30.

#### D. What is the total price including tax?
# Explanation:
## Step1: Recall the total price formula
The total price including tax is the sum of the sale price and the sales tax. The formula is: $ \text{Total Price} = \text{Sale Price} + \text{Sales Tax} $

We know the sale price is $54.99 and the sales tax (from part C) is approximately $3.30.

## Step2: Substitute the values into the formula
$ \text{Total Price} = 54.99 + 3.30 $

## Step3: Calculate the result
$ 54.99 + 3.30 = 58.29 $

# Answer:
The total price including tax is $58.29.

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QUESTION IMAGE

Question

Explanation:

3. iPhone 16

A. How much did the price change?

Step1: Subtract sale price from original price

Step2: Calculate the result

Step1: Recall the percent change formula

Step2: Substitute the values into the formula

Step3: Calculate the fraction first

Step4: Multiply by 100% to get the percentage

Step1: Recall the sales tax formula

Step2: Substitute the values into the formula

Step3: Calculate the result

Answer:

B. What is the percent of change?