Question

Find the percentage change in price in each of the following examples using the mid-point method.

Instructions: Round your answers to two decimal places. If you are entering a negative number be sure to include a negative sign (-) in front of that number.
a. The price of a $4 sandwich increases to $5: percent
b. A sale discounts the price of a sofa from $750 to $500: percent

Answer 1

The percentage change in the price of the sandwich using the midpoint method is 22.22%, and the percentage change for the sofa is -40.00%.

Step-by-step explanation:

To find the percentage change in price using the midpoint method, you calculate the price change divided by the average price (the midpoint between the old and new prices) and then multiply by 100 to convert it to a percentage.

a. The price of a $4 sandwich increases to $5:

• Change in price = $5 - $4 = $1
• Midpoint (average price) = ($4 + $5) / 2 = $4.50
• Percentage change = ($1 / $4.50) × 100 = 22.22%

b. A sale discounts the price of a sofa from $750 to $500:

• Change in price = $500 - $750 = -$250 (negative because the price decreased)
• Midpoint (average price) = ($750 + $500) / 2 = $625
• Percentage change = (-$250 / $625) × 100 = -40.00%

Answer 2

0.22

-0.40

Step-by-step explanation:

midpoint change in price = change in price / average of both price

a. change in price = (5 - 4) = 1

average of both prices = 0.5 (4 + 5) = 4.50

midpoint change in price = 1/ 4.5 = 0.22

b. change in price = (500 - 750) = -250

average of both prices = 0.5(750 + 500) = 625

-250 / 625 = -0.4