Problem 1 - Algebra 1

Question

Write an equation that represents the statement "10\% of 160 is 16." What is the base number?

Step-by-Step Solution

Answer

The base number is 160.

Step 1: Write the Statement as an Equation

From the statement '10% of 160 is 16', we can formulate it into an equation by substituting respective percentages and numbers. We can write it as \(0.10 \times X = 16\) where X is the base number.

Step 2: Identifying the base number

The base number is what the percentage is taken of. In this case, the base number is mentioned in the statement itself which is 160. So, X is 160.

Step 3: Checking the Solution

To ensure the answer is correct, we put X = 160 in equation which gives \(0.10 \times 160\). Calculating this, we get 16 which is in agreement with the statement.

Key Concepts

Understanding Algebraic Equations

An algebraic equation is a mathematical statement that uses variables, numbers, and operational symbols to represent a relationship.
In this case, the statement "10% of 160 is 16" can be turned into an algebraic equation to find unknown elements like the base number. The statement involves a percentage calculation, which is a common scenario in real-world problems. To express this mathematically, we use variables. Letting the variable be the base number, we can write the equation as follows:

• The percentage, 10%, is written as a decimal: 0.10.
• The expression becomes: \(0.10 \times X = 16\).

Using algebraic manipulation, one can solve for the variable to uncover unknown values or to verify given conditions.

The Role of the Base Number

In percentage problems, the base number is the amount that the percentage value is derived from. Think of it as the starting point or the whole from which a part is calculated.
In the exercise statement "10% of 160 is 16," 160 is identified as the base number. Identifying the base number is essential:

• It is the number upon which the percentage calculation is based.
• Recognizing this allows one to properly set up algebraic equations.

In this example, the keyword "of" typically indicates the number that follows is the base when it comes to percentages, leading us to isolate 160 for calculation.

Crafting a Step-by-Step Solution

Breaking down a problem through a step-by-step solution is crucial for clarity, especially in mathematical exercises. This method ensures each aspect of the problem is addressed methodically.For this exercise, the steps include:

• **Step 1:** Translate words to an equation. Convert the percentage into a decimal and construct the equation as \(0.10 \times X = 16\).
• **Step 2:** Identify the base number from the statement: here, 160 directly suggests itself as the base of the percentage.
• **Step 3:** Verify the result by plugging the base number back into the original equation. Re-evaluating \(0.10 \times 160\) confirms the answer as 16.

This sequential breakdown helps ensure understanding and accuracy at each stage.