Question

If \(85 \%\) of stock is sold, how much stock did we start with if 120 items remain? A. 800 B. 680 C. 18 Answer D. 120 E. 750

Short answer

The original stock is 800.

Step-by-step solution

Understanding the problem

Determine what portion of the stock remains if 85% has been sold. This means 15% of the stock is left because 100% - 85% = 15%.

Set up the equation

Let the original amount of stock be denoted as \( x \). Since 15% of the stock remains, we can write the equation as \[ 0.15x = 120 \]

Solve for the original stock

Isolate \( x \) by dividing both sides of the equation by 0.15: \[ x = \frac{120}{0.15} = 800 \]

Verify the solution

Verify by calculating 15% of 800, which should equal 120: \[ 0.15 \times 800 = 120 \]. The calculation confirms that our solution is correct.

Identify the correct answer

From the options given, option A, 800, is the correct answer.

Key concepts

Percentage Problems

Let's break down the concept of percentage problems. Percentages are a way to express a number as a part of a whole. In our problem, we need to find out the whole (original stock) when we're given a part of it (remaining stock).

This type of problem typically involves:

• Identifying the total percentage (here, 100%).
• Calculating the percentage of stock sold and remaining. Since 85% is sold, we have 15% left (100% - 85%).

So, we're essentially dealing with 15% and solving for the total when we know 120 items equal 15%.

Algebraic Equations

Algebraic equations are a way to represent relationships using mathematical symbols. In this problem, we use an equation to express the relationship between the original stock and the remaining stock.

We start by letting the original stock be represented by a variable, let's call it \( x \). We know 15% of this stock remains, so we set up the equation: 0.15x = 120.

This equation means that 15% of the original stock (0.15x) equals 120 items. Solving this equation gives us the original stock quantity.

Problem-Solving Steps

Problem-solving in math follows a logical series of steps:

• Understand the problem: We identified that 15% of the stock remains.
• Set up the equation: Using the percentage given, we created the equation 0.15x = 120.
• Solve the equation: We isolated \( x \) by dividing both sides of the equation by 0.15.
• Verify the solution: We checked our answer by calculating 15% of 800, which indeed is equal to 120.
• Identify the correct answer: Finally, we confirmed our solution matched one of the given options.

These steps ensure a systematic approach to solving not just this problem, but any similar percentage problems.