Problem 112 - Elementary Algebra

Question

The price of a share of one stock rose from \(\$ 12.50\) to \(\$ 50\). Find the percent increase.

Step-by-Step Solution

Answer

The percent increase is 300%.

Step 1 - Determine the initial and final prices

Identify the initial price of the stock, which is \$12.50$$, and the final price of the stock, which is \$50.00$$.

Step 2 - Calculate the increase in price

Subtract the initial price from the final price to find the increase. \[ 50.00 - 12.50 = 37.50 \]

Step 3 - Find the ratio of increase to the initial price

Divide the increase in price by the initial price. \[ \frac{37.50}{12.50} = 3 \]

Step 4 - Convert the ratio to a percentage

Multiply the ratio by 100 to get the percentage increase. \[ 3 \times 100 = 300\% \]

Key Concepts

initial price

In any percentage increase calculation, it's essential to pinpoint the starting point. This is what we call the 'initial price'. Imagine you are buying stock. The initial price is how much each share costs at the beginning. In our example, the initial price of the stock was \(\$12.50\)\. This initial price acts as the baseline for any calculations we will perform. Essentially, it's our reference point to determine how much the price has changed.

final price

After identifying the initial price, the next step is to determine the 'final price'. This is the new price after a certain period or event. In the given exercise, the final price of the stock is \(\$50\)\. Comparing this final price with the initial price will help us understand how much the price has increased. The final price always gives us a sense of the current value, which is crucial for our next steps in calculation.

price increase

Once we have both the initial and final prices, we can calculate the 'price increase'. This is the actual dollar amount that the price has risen by. To find this, you subtract the initial price from the final price: \(50 - 12.50 = 37.50\). So, in our example, the price increase is \(37.50\) dollars. This value forms the basis for calculating the percentage increase.

percentage increase

Finally, to understand the 'percentage increase', we need to convert the price increase into a percentage. First, divide the price increase by the initial price: \(\frac{37.50}{12.50}=3\). This result represents the ratio of the increase relative to the initial price. To convert this ratio into a percentage, multiply it by 100: \(3 \times 100 = 300\%\). This means the price of the stock increased by 300\% from its initial price. Percentages make it easier to compare the rate of increase relative to different initial prices visually.