Problem 83 - Elementary Algebra

Question

Tanya bought 400 shares of one stock at \(\$ 14.78\) per share, and 250 shares of another stock at \(\$ 16.36\) per share. How much did she pay for the 650 shares?

Step-by-Step Solution

Answer

Tanya paid \( \$ 10002 \) for the 650 shares.

Step 1: Calculate Cost of First Stock

First, we need to find out how much Tanya paid for the 400 shares she bought. Each share costs \( \\( 14.78 \). Therefore, the total cost for the 400 shares is calculated as follows: \( 400 \times 14.78 \). Performing the multiplication: \( 400 \times 14.78 = 5912 \). Thus, Tanya paid \( \\) 5912 \) for the first stock.

Step 2: Calculate Cost of Second Stock

Next, calculate the cost for the 250 shares of the second stock. Each share costs \( \\( 16.36 \). The total cost for these shares is calculated as: \( 250 \times 16.36 \). By multiplying these figures: \( 250 \times 16.36 = 4090 \). Thus, Tanya paid \( \\) 4090 \) for the second stock.

Step 3: Compute Total Cost for Both Stocks

Finally, add the total costs of both stocks to find out how much Tanya paid for all 650 shares. The sum of the costs is: \( 5912 + 4090 \). Adding them together gives us: \( 5912 + 4090 = 10002 \). Therefore, Tanya paid \( \$ 10002 \) for all the shares she bought.

Key Concepts

Multiplication in Algebra

When we talk about multiplication in Algebra, especially in the context of word problems, we're dealing with operations that help us find total amounts or multiplicative relationships. In Tanya's problem, we used multiplication to determine how much she spent on stocks. Here's how it works:

• Understand the problem. Identify that Tanya purchased 400 shares of one stock, with each share costing \( \$14.78 \).
• To find the total cost of these shares, multiply the number of shares (400) by the price per share (\(14.78\)).
• Perform the calculation: \( 400 \times 14.78 = 5912 \).

This calculation shows the total expenditure on the first set of stocks. Multiplication helps convert the problem into a simple arithmetic operation. When you understand this, you can apply it to any similar problem, regardless of the context.

Addition of Decimal Numbers

Addition of decimal numbers is an important mathematical skill, especially in calculations involving money, like in the stock market problem. Here are the basics you should remember:

• Make sure decimal points are aligned. This keeps the values in the correct place, ensuring accurate addition.
• In Tanya’s case, after computing the individual costs, \(5912\) from the first stock and \(4090\) from the second, align the numbers: \[ \begin{align*} &5912 \ + &4090 \ \hline \end{align*} \]
• Add digit by digit, starting from the rightmost digit (units place) moving left: - Units: 2+0=2, - Tens: 1+9=10 (place 0, carry 1), - Hundreds: 9+0=9+carry 1 =10 (place 0, carry 1), - Thousands: 5+4=9+carry 1 = 10.
• Write down the total, \(10002\), as the complete cost.

By ensuring careful alignment and adding systematically, dealing with decimals becomes straightforward.

Stock Market Problems

Stock market problems are common in algebra word problems as they combine real-world scenarios with mathematical operations. In Tanya's situation, understanding stocks is key:

• Stocks are shares or parts of a company that can be bought. In this problem, Tanya invested in two different stocks with different prices per share.
• For financial calculations like this, it's essential to know how to determine total costs of multiple purchases. This involves multiplication (to find costs of each stock) and addition (to find the overall cost).
• Being able to understand and solve these problems gives practical insight into managing finances and investments.

Stock market exercises not only test mathematical skills but also develop financial literacy. Mastering these problems could enhance understanding of market trends and investment strategies.