Question

Given a percent of decrease and an initial amount, explain how to find the final amount after the decrease. In July, a company's total expenses were \(\$ 12,250\). In August, the company cut costs by 4\%. How much were the costs reduced? What amount did the company spend in August?

Short answer

Answer: The company spent $11,760 in August.

Step-by-step solution

Convert the percentage decrease into a decimal value

In this situation, the percentage decrease is 4%, which can be expressed as a decimal value by dividing 4 by 100. So, the decimal equivalent of 4% is: $$ \frac{4}{100} = 0.04 $$

Calculate the decrease in cost

Next, calculate the decrease in the company's total expenses by multiplying the initial amount with the decimal equivalent of the percentage decrease: $$ Decrease = InitialAmount \times DecimalPercentage $$ $$ Decrease = \$ 12,250 \times 0.04 $$ $$ Decrease = \$ 490 $$ So, the company's costs were reduced by $490.

Calculate the final amount after decrease

Lastly, calculate the amount the company spent in August by subtracting the decrease in cost from the initial amount: $$ FinalAmount = InitialAmount - Decrease $$ $$ FinalAmount = \$ 12,250 - \$ 490 $$ $$ FinalAmount = \$ 11,760 $$ Thus, the company spent \( \$11,760\) in August after cutting costs by 4%.

Key concepts

Understanding Percentage Decrease

Percentage decrease explains how much a quantity has lessened in terms of percentage. This concept is essential in various real-life contexts such as finance, shopping discounts, or changes in expenses. Simply put, it tells us by what percent an amount has gone down.

• To calculate the percentage decrease, start by identifying the percent you want to decrease the original amount by. For example, in this exercise, we have a 4% decrease.
• Next, convert this percentage into a decimal by dividing by 100. Thus, 4% becomes 0.04.
• This conversion is crucial because it allows you to use this value directly in further calculations.

By understanding percentage decrease, you can effectively determine how much lesser the new amount will be compared to the original.

The Initial Amount

The initial amount is the starting value or the original figure before any changes have occurred. It forms the basis upon which the calculations for percentage increase or decrease are performed.

• In this exercise, the initial amount is the company's total expenses in July, which was $12,250.
• Knowing the initial amount is crucial because it acts as the standard or reference point for determining the decrease.
• Every calculation of the percentage decrease or increase will begin with the initial amount.

Therefore, it is important to accurately identify the initial amount whenever you are calculating percentage decrease to ensure your results are reliable.

Calculating the Final Amount After Decrease

Once you have computed the amount of decrease, the next step is to find out what the final amount will be. This final amount refers to the new value after the original amount has been reduced by the derived decrease.

• First, determine the total decrease by multiplying the initial amount by the converted decimal percentage. In our example, this was a decrease of \( \\(490 \).
• The final amount is then found by subtracting this decrease from the initial amount. In the exercise, we calculated it as \( \\)12,250 - \\(490 = \\)11,760 \).
• This result gives the actual expenses for the following period, post-decrease.

Remember, the correct calculation of the final amount offers a practical understanding of how percentage decreases affect real-world numbers, such as company expenses in different months.