Problem 74 - Algebra 1

Question

GOLD PRICES IN LONDON At 9 A.M., an ounce of gold sells for \(\$ 287.56\). At noon, gold sells for \(\$ 286.90\) per ounce. At 4 P.M., the final price for the day is \(\$ 287.37\) per ounce. What is the change in the price per ounce of gold from noon to 4 P.M.?

Step-by-Step Solution

Answer

The change in the price per ounce of gold from noon to 4 P.M. is \( \$ 0.47 \).

Step 1: Identifying the relevant prices

The problem asks for the change in the price per ounce of gold from noon to 4 P.M. The price at noon is \( \$ 286.90 \) and the price at 4 P.M. is \( \$ 287.37 \).

Step 2: Calculating the price change

To calculate the price change, subtract the price at noon from the price at 4 P.M. Therefore, \( \$ 287.37 - \$ 286.90 = \$ 0.47 \).

Key Concepts

Price Change Calculation

Price change calculation is an essential aspect of understanding daily commodity fluctuations like gold prices. It involves determining how much the price of an item has increased or decreased over a period. In our gold price scenario, we're focusing on the change in price from noon to 4 P.M.
The key steps to perform a price change calculation include:

• Identifying the initial price, which is the price at the start of the period. In this case, the gold price at noon is $286.90.
• Identifying the final price, which is the price at the end of the period. Here, it's $287.37 at 4 P.M.
• Subtracting the initial price from the final price to find the difference.

Understanding the price change helps investors and consumers make informed decisions based on market trends. It is often used in various market analyses to gauge profitability or loss.

Subtraction

Subtraction is the primary mathematical operation used to calculate the difference between two quantities. In algebraic problem-solving, subtraction plays a vital role as it helps find changes between values, such as calculating price differences.

In the gold price problem, subtraction helps determine the price change by taking the following steps:

• Take the final price: \(287.37
• Take the initial price: \)286.90
• Perform the subtraction: \( 287.37 - 286.90 = 0.47 \)

This result, 0.47, shows the amount the gold price increased from noon to 4 P.M.
Subtraction is fundamental not only in classrooms but also in financial contexts, where accurate calculations ensure precise financial assessments.

Real-World Application

The gold price scenario demonstrates the real-world application of algebraic problem-solving techniques. Price changes in commodities like gold have direct implications for both individual investors and broader economic trends.
Using simple mathematical operations such as subtraction to understand price changes is a real-world application of algebra. This scenario can be applied to several situations individuals face daily, such as:

• Comparing fuel prices from one day to another.
• Understanding stock market changes over time.
• Tracking expenses to manage budgets better.

These applications underscore how basic algebra and arithmetic remain relevant and necessary for making everyday decisions based on financial and economic conditions. By grasping these concepts, students are equipped to analyze and interpret data they encounter in their daily lives effectively.