Problem 113 - Elementary Algebra

Question

According to Time magazine annual \(\quad\) global seafood consumption rose from 22 pounds per person in the \(1960 \mathrm{~s}\) to 38 pounds per person in 2011 . Find the percent increase. (Round to the nearest tenth of a percent.)

Step-by-Step Solution

Answer

72.7%

Step 1: Identify Initial and Final Values

Identify the initial value and the final value from the problem. The initial value is 22 pounds per person, and the final value is 38 pounds per person.

Step 2: Calculate the Increase

Find the difference between the final value and the initial value: Final value − Initial value = 38 − 22 = 16 pounds

Step 3: Determine the Relative Increase

Divide the increase by the initial value to calculate the relative increase: Relative increase = Increase ÷ Initial value = 16 ÷ 22 ≈ 0.7273

Step 4: Convert to Percentage

Multiply the relative increase by 100 to convert it to a percentage: Percentage increase ≈ 0.7273 × 100 = 72.73%

Step 5: Round to the Nearest Tenth

Round the percentage increase to the nearest tenth of a percent: 72.73% rounded to the nearest tenth is 72.7%

Key Concepts

initial value

To begin any percentage increase calculation, you need to identify the initial value. The initial value is the starting point or the original quantity before any change occurs. In our exercise, this is the amount of seafood consumed per person in the 1960s, which is 22 pounds. Understanding the initial value is crucial because it serves as the baseline to which we compare the final value. Without a clear initial value, it is impossible to accurately measure any increase or decrease.

final value

The final value represents the new quantity after the change has taken place. In this case, it's the global seafood consumption per person in 2011, which is 38 pounds. The final value is compared against the initial value to determine how much change has occurred. By comparing the final value of 38 pounds to the initial value of 22 pounds, we can see that there has been an increase in seafood consumption over the period. Understanding the final value helps in calculating the difference from the initial value, which is essential for determining the percentage increase.

relative increase

The relative increase shows how much more the final value is compared to the initial value, expressed as a ratio or fraction. To find it, you subtract the initial value from the final value to get the total increase. Here, the increase is 38 - 22 = 16 pounds. Next, you divide the increase by the initial value: 16/22 ≈ 0.7273. This ratio tells us that the final value is about 72.73% more than the initial value. The concept of relative increase helps put the change in perspective, making it easier to understand the extent of the change relative to the starting point.

rounding percentages

Rounding percentages is often necessary for simplicity and easier communication of results. To round a percentage to the nearest tenth, you look at the digit in the hundredths place. In our example, the relative increase was about 72.73%. Here, the hundredths place is '3'. Since it's less than 5, we round down, keeping the tenths place unchanged. Thus, 72.73% rounds to 72.7%. Rounding makes numbers easier to read and understand, especially in situations where too many decimal places would be cumbersome or unnecessary.