Problem 52 - Algebra 1

Question

Solve the percent problem. 1240 is \(80 \%\) of what number?

Step-by-Step Solution

Answer

The whole number is 1550.

Step 1: Understand the Problem

From the problem, we know that 1240 is 80% of some number. The task is to find that number.

Step 2: Set Up The Equation

The general formula to solve such problems is \( \text{Part} = \text{Percent} \times \text{Whole} \), we can rearrange it as \(\text{Whole} = \frac{\textup{Part}}{\textup{Percent}} \). Here, Part=1240 and Percent=80% or 0.80 in decimal form.

Step 3: Calculate The Whole Number

Substitute Part and Percent into the equation, we get \( \text{Whole} = \frac{1240}{0.80} \)

Step 4: Solve for the Whole Number

By doing the division, we find that the whole number is 1550

Key Concepts

Equation Solving

When faced with a math problem, a structured approach to solving equations is key. Start by understanding what the equation represents in the context of the problem. For example, if you're trying to find a number where 80% equals 1240, you need to express this relationship mathematically. The equation typically involves identifying variables and constants. You may find it helpful to substitute known values into an algebraic equation, then solve for the unknown. In this case, you rearrange the percent formula into an equation that helps find the number you're looking for: \[\text{Whole} = \frac{\text{Part}}{\text{Percent}}\]Here, your target is to solve for the 'Whole'. By substituting 1240 for Part and 0.80 for Percent, division simplifies your task, resulting in the desired value.

Percent Formulas

Percent formulas are indispensable tools in everyday mathematics. They help in determining parts of a whole, calculating discounts, and understanding increases or decreases in values. The basic percent formula relates three parts: the Part, Whole, and the Percent:\[\text{Part} = \text{Percent} \times \text{Whole}\]To solve percent problems, you often rearrange this formula to find the unknown. For example, determining what 'Whole' number 1240 is 80% of, uses a variation of this formula: \[\text{Whole} = \frac{\text{Part}}{\text{Percent}}\]This formula changes depending on what you are solving for:

• Use \(\text{Whole} = \frac{\text{Part}}{\text{Percent}}\) when finding the Whole.
• Use \(\text{Percent} = \frac{\text{Part}}{\text{Whole}}\) when finding the Percent.
• Use \(\text{Part} = \text{Percent} \times \text{Whole}\) when finding the Part.

Understanding these formulas helps in effectively tackling percent problems with ease.

Algebraic Expressions

Algebraic expressions are fundamental components of algebra, consisting of variables, numbers, and operation symbols. They express mathematical relationships concisely and accurately. For example, in a percent problem, an algebraic expression represents the relationship between the Part, Percent, and Whole.An expression like:\[\text{Whole} = \frac{\text{Part}}{\text{Percent}}\]shows how to structure information from a word problem into a solvable mathematical format. Variables such as Part and Percent stand in for numerical values and allow for a general, reusable solution approach.Getting comfortable with algebraic expressions equips you to translate word problems into mathematical equations, making solving them more straightforward. Remember the key is understanding each part of the expression and what it represents in your problem.