Problem 120 - Elementary Algebra

Question

Sales of video games and consoles fell from \$1,150 million to \(\$ 1,030\) million in 1 year. Find the percent decrease. (Round to the nearest tenth of a percent.)

Step-by-Step Solution

Answer

The percent decrease is 10.4%.

Step 1: Identify Initial and Final Values

The initial value of the sales is \(1,150 million and the final value is \)1,030 million.

Step 2: Calculate the Decrease in Sales

Subtract the final value from the initial value to find the decrease: ecrease = Initial Value - Final ValueDecrease = 1,150 - 1,030 = 120 million.

Step 3: Calculate the Percent Decrease

Divide the decrease by the initial value, then multiply by 100 to convert it to a percentage: \(\text{Percent Decrease} = \frac{Decrease}{Initial Value} \times 100\)\(\text{Percent Decrease} = \frac{120}{1150} \times 100 \approx 10.4\)

Step 4: Round to the Nearest Tenth

Round 10.4 to the nearest tenth. Since it is already at the nearest tenth, the final answer is 10.4%.

Key Concepts

Percent Change

Percent change is a very useful concept in elementary algebra. It helps us understand how much a quantity has increased or decreased in terms of percentages.
In this exercise, we are dealing with a **percent decrease**. A percent decrease tells us how much a value has gone down over time, compared to its initial value. To calculate it, we:

• Find the initial value, which is the starting amount.
• Find the final value, which is the amount after the change.
• Subtract the final value from the initial value to find the decrease.
• Divide the decrease by the initial value, then multiply by 100 to convert it to a percentage.

For example, if video game sales dropped from \$1,150 million to \$1,030 million, you would find the decrease, which is \$120 million, and then use the percent change formula: \(\text{Percent Decrease} = \frac{Decrease}{Initial Value} \times 100\). This would give you approximately 10.4%.

Decrease Calculation

Understanding how to calculate a decrease is essential in many math problems. Decrease calculation is simply finding out how much a number has been reduced.
Given the initial and final values, the steps are:

• Subtract the final value from the initial value to find the decrease.
• This gives you the amount that has been lost or reduced.

For instance, if sales dropped from \$1,150 million to \$1,030 million, subtract the final value from the initial value: \[Decrease = Initial Value - Final Value = 1,150 - 1,030 = 120 \text{ million} \] This means the sales decreased by \120 million dollars in one year.
It is important to make sure you subtract correctly and understand the context of the numbers, to make sure you are calculating the correct decrease.

Elementary Algebra

Elementary algebra involves basic algebraic concepts that form the foundation for more advanced math. One core concept is working with percentages and understanding how to apply them to real-world problems.
In our scenario, we calculated the percent decrease of video game sales. This involved:

• Grasping basic percentage concepts.
• Performing subtraction accurately.
• Using division and multiplication correctly to find the percentage.

The formula for percent decrease is a part of elementary algebra that helps you handle many practical problems. To reiterate, the formula used is: \[ \text{Percent Decrease} = \frac{\text{Decrease}}{\text{Initial Value}} \times 100 \] By understanding these steps, students can apply this knowledge to various situations, such as financial changes, population studies, and more.