Problem 22 - Elementary Algebra

Question

Solve the following problems. Eight percent of a number is 1.2 . What is the number?

Step-by-Step Solution

Answer

Answer: The unknown number is 15.

Step 1: Set up the proportion

Start by representing the problem as an equation: 0.08 * x = 1.2 Here, x represents the unknown number, and 0.08 (or 8%) is the proportion that represents 8% of the number.

Step 2: Solve for x

Now, we need to isolate x. Since 0.08 is multiplied by x, we will divide both sides by 0.08: x = \frac{1.2}{0.08}

Step 3: Simplifying the expression

Divide 1.2 by 0.08 to get the value of x: x = 15 So, the unknown number is 15.

Key Concepts

Proportion

In mathematics, a proportion is a statement that signifies two ratios are equal. Proportions allow us to represent relationships in simple equations that can predict unknown values. For instance, when we say that eight percent of a number is equal to 1.2, we are utilizing a proportional relationship. Here, the 8% can be expressed in its decimal form, 0.08, which is crucial when setting up the mathematical equation. This proportional relationship between parts and the whole makes problem-solving intuitive and systematic.

• Understanding proportions helps solve real-world problems involving parts of a whole.
• They provide a simple method to work with percentages, fractions, and ratios.
• Proportions are the foundation of scaling problems, such as scaling recipes or maps.

Knowing how to structure a problem as a proportion is a valuable skill. It allows us to convert complex problems into familiar equations that we can solve with ease.

Solving Equations

Solving equations is at the heart of mathematics. It is the process by which we find the value(s) of the variable(s) that make an equation true. When presented with the equation 0.08 * x = 1.2, the goal is to isolate the variable 'x' on one side of the equation to discover its value.
To do this:

• Identify what is being done to the variable and do the opposite operation to both sides of the equation.
• Here, multiplication is reversed by division. Dividing both sides of the equation by 0.08 facilitates isolating 'x'.
• This practice is known as balancing the equation, ensuring that both sides remain equal.

Solving equations teaches logical thinking and reinforces the understanding that any operation done to one side of an equation must be done to the other to maintain equality. This methodical approach ensures accuracy while solving mathematical problems.

Algebraic Expressions

An algebraic expression is a combination of numbers, variables, and arithmetic operations. These expressions can be as simple as a single number, or as complex as a large combination of variables and constants. In our problem, 0.08 * x = 1.2 is an algebraic expression involving a multiplication of a number and a variable.
The key parts of working with algebraic expressions include:

• Understanding that letters, like 'x', represent unknown values that we aim to find.
• Using arithmetic operations to express relationships between known and unknown quantities.
• Simplifying expressions by combining like terms or using mathematical operations to solve for variables.

Mastering algebraic expressions allows for solving equations and understanding complex relationships in mathematics. It also serves as a powerful tool for modeling real-life situations, providing a pathway to find solutions efficiently and logically.