Problem 65 - Elementary and Intermediate Algebra

Question

Translate each problem to an equation. Do not solve. When 42 is multiplied by a number, the result is 2352 . Find the number.

Step-by-Step Solution

Answer

\[ 42x = 2352 \]

Step 1: Identify the given information

The problem provides two pieces of information: the number 42 and the result 2352.

Step 2: Let the unknown be a variable

Represent the unknown number by a variable. For instance, let the unknown number be represented by the variable \( x \).

Step 3: Set up the equation

To translate the problem into an equation, use the information given. The problem states that when 42 is multiplied by a number \( x \), the result is 2352. This can be written as: \[ 42x = 2352 \].

Key Concepts

unknown variable

Many word problems in math involve an unknown quantity that we need to find. This unknown quantity is often represented by a variable, usually a letter like 'x' or 'y'. In our exercise, we need to find a number when multiplied by 42 gives 2352. This unknown number can be represented by the variable 'x'.
This is a common technique to simplify and translate word problems into equations. Identifying the unknown variable is a crucial first step because it allows us to transform everyday language into mathematical language.

setting up equations

Once we have identified the unknown variable, the next step is to use the given information to set up an equation. This involves translating the words of the problem into a mathematical statement. In our exercise:

• The phrase 'when 42 is multiplied by a number' means we are performing a multiplication operation between 42 and our variable 'x'.
• The phrase 'the result is 2352' tells us the outcome of this multiplication is 2352.

Combining these pieces, we can write the equation as n n n n n n Create Equations: n The crucial step in setting up equations is accurately translating the problem's words into mathematical expressions. Misinterpretation can lead to incorrect equations and final results.

problem-solving steps

Problem-solving in math involves a series of well-structured steps to find an unknown quantity. The steps followed in our example are straightforward and apply to a wide range of problems.

• Step 1: Identify the Given Information
  Start by noting down all the numbers and details provided in the problem.
• Step 2: Define the Unknown Variable
  Use a variable like 'x' to represent the unknown number or quantity in the problem.
• Step 3: Set up the Equation
  Translate the problem's words into a mathematical equation using the identified information and variable.

For our problem, these steps helped us form the equation n n n n n n A structured approach like this ensures that you don't miss any information, queue, or step while solving math problems. Practice using these steps, and soon, solving word problems will become second nature!