Problem 46 - Algebra for College Students

Question

Solve each percent problem. In \(2016,\) the average cost of a Thanksgiving turkey was \(\$ 22.74 .\) This price had decreased by \(1.58 \%\) in \(2017 .\) What was the average cost of a Thanksgiving turkey in \(2017 ?\)

Step-by-Step Solution

Answer

\$22.38 (rounded to nearest cent)\.

Step 1 - Identify the initial value and the percentage decrease

The initial cost of the Thanksgiving turkey in 2016 was \( \$22.74 \). The percentage decrease in price in 2017 was \( 1.58\% \).

Step 2 - Convert the percentage decrease to a decimal

To convert the percentage decrease to a decimal, divide by 100: \( 1.58 \div 100 = 0.0158 \)

Step 3 - Calculate the amount of decrease

Multiply the original cost by the decimal: \( 22.74 \times 0.0158 = 0.359292 \). So, the decrease in price is \$0.3593\ (rounded to four decimal places).

Step 4 - Subtract the decrease from the original cost

Subtract the decrease from the original price: \( 22.74 - 0.3593 = 22.3807 \). Therefore, the cost of the Thanksgiving turkey in 2017 was \

Key Concepts

percentage decrease

Understanding percentage decrease is crucial when analyzing how values change over time. To calculate percentage decrease, you first need to understand what it represents. It shows how much a value has dropped in comparison to its original amount. For example, if a turkey costs \(22.74 in 2016 and its price decreased by 1.58% in 2017, we can find the new cost by following a few steps. First, identify the initial value, which is \)22.74. The percentage decrease is 1.58%. To find the actual decrease amount, convert this percentage into a decimal and multiply it by the original value.

decimal conversion

Decimal conversion is an essential step in many mathematical operations, including percentage problems. Converting a percentage into a decimal makes it easier to perform calculations. To convert a percentage to a decimal, divide by 100. For instance, 1.58% becomes 0.0158 when divided by 100. This decimal form can now be used in further mathematical operations. Remember, shifting the decimal point two places to the left achieves the same result. Thus, 1.58% turns into 0.0158.

cost calculation

Cost calculation involves determining the new value of an item after a percentage change. Once you have the decimal form of the percentage decrease, you can calculate the amount of decrease by multiplying the original cost with the decimal. For example, if the original cost of the turkey is \(22.74 and the percentage decrease is 1.58%, then multiply \)22.74 by 0.0158 to find the decrease amount. That gives you approximately \(0.36. Finally, subtract this value from the original cost to get the new price: \)22.74 - \(0.36 = \)22.38. This is the new cost of the turkey for 2017, considering the 1.58% decrease.

mathematical operations

Mathematical operations are steps we perform to solve problems. For percentage decrease, these operations include division, multiplication, and subtraction. First, convert the percentage to a decimal by dividing by 100 (division). Second, find the decrease amount by multiplying the original price by this decimal (multiplication). Finally, subtract the decrease amount from the original price (subtraction). For instance, from \(22.74, if the decrease is \)0.36, the final operation will be \(22.74 - \)0.36, giving $22.38. These simple operations help in straightforwardly calculating new values after percentage changes.