Problem 44 - Algebra for College Students

Question

Solve each percent problem. On Major League Baseball Opening Day \(2016,\) the payroll of the Cleveland Indians was \(\$ 87.2\) million. In 2017 , it had increased \(44.3 \%\). To the nearest tenth of a million, what was the opening-day payroll of the Indians for \(2017 ?\)

Step-by-Step Solution

Answer

The payroll for 2017 was approximately \125.8\text{ million}.

Step 1 - Understand the Problem

First, identify the given values in the problem. The original payroll in 2016 was \(\$87.2 \) million, and the increase percentage in 2017 was \44.3\text{\%} \.

Step 2 - Convert Percentage to Decimal

To find the increase amount, convert the percentage to a decimal. Percentage values must be divided by 100 to convert them to decimals: \( 44.3\text{\%} = 0.443 \).

Step 3 - Calculate the Increase Amount

Multiply the payroll amount in 2016 by the decimal value to find the increase: \( 87.2 \times 0.443 = 38.6096 \text{ million} \).

Step 4 - Calculate the 2017 Payroll

Add the increase amount to the original payroll to find the payroll for 2017: \( 87.2 + 38.6096 = 125.8096 \text{ million} \).

Step 5 - Round to the Nearest Tenth

Round the payroll amount in 2017 to the nearest tenth of a million: \( 125.8096 \approx 125.8 \text{ million} \).

Key Concepts

percentage conversion

A key step in many math problems is converting percentages to decimals. This conversion is essential because it allows us to perform multiplication and other arithmetic operations directly. To convert a percentage to a decimal, simply divide the percentage by 100. For example, in the given exercise, 44.3% is converted to a decimal by calculating 44.3 ÷ 100, which equals 0.443. This step is critical in making calculations straightforward.

decimal multiplication

Once you have converted a percentage to a decimal, you can use it in multiplication to find increases or decreases. In our exercise, we needed to calculate the increase in payroll, given as a 44.3% increase on \(87.2 million. By converting 44.3% to 0.443 and multiplying by \)87.2 million, we find the increase: 87.2 × 0.443 = 38.6096 million. Multiplication with decimals follows the same rules as whole numbers, but you need to keep track of decimal places.

rounding decimal

Rounding decimals is an important skill, especially when you need to report answers in a specific format. In this exercise, we needed to round the final payroll amount to the nearest tenth. The final computed amount was \(125.8096 million. To round to the nearest tenth, focus on the first decimal place (tenths place). If the following digit (hundredths place) is 5 or greater, we round up. In this case, 0.8096 is rounded to 0.8, making the rounded payroll \)125.8 million.

payroll calculation

Payroll calculations often involve percent increases, such as annual raises. This exercise illustrates how to handle such increases. First, identify the original and the percentage increase. Convert the percentage to a decimal, multiply to find the increase, then add that to the original value. Lastly, rounding may be required to match the desired reporting format. For the Cleveland Indians, starting with \(87.2 million and applying a 44.3% increase, we computed the new payroll as \)125.8 million after rounding.