Problem 95 Translate each problem to an equ... [FREE SOLUTION]

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Chapter 15: Problem 95

Translate each problem to an equation. Do not solve. Three times what number is \(348 ?\)

Short Answer

Expert verified

3x = 348

Step by step solution

Identify the unknown number

Let the unknown number be represented by the variable \( x \).

Express 'three times the number'

The phrase 'three times the number' can be translated into the expression \( 3x \).

Set up the equation

We know that three times the unknown number equals 348, so we can write the equation as \( 3x = 348 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

algebraic expressions

Algebraic expressions are a key part of algebra and allow us to represent mathematical ideas concisely. In this exercise, we encounter the phrase 'three times what number'. To translate this into algebra, we use basic operations and numbers. For example, if we want to express 'three times a number', we can use multiplication. Here's what it looks like:

The phrase 'a number' is our unknown and can be represented by a variable, such as x.
'Three times' means we multiply the unknown number by 3.

Putting this together, 'three times a number' translates to the algebraic expression:
n 3x .

variables

Variables are symbols used to represent unknown values in mathematical expressions and equations. In algebra, we often use letters like x, y, and z as variables. They make it easier to set up and solve problems.
In this exercise, we use the variable x to represent an unknown number. The steps are:

Choose a variable (in this case, x) to represent the unknown.
Use this variable consistently throughout the problem.

For instance, in our problem, 'three times what number is 348?', we chose x to represent 'what number'. Then, 'three times what number' becomes 3x.
This helps us translate word problems into math, making them easier to solve.

setting up equations

Setting up equations is a crucial step in solving word problems. It involves translating the words into mathematical language. In this exercise, we follow these steps:

Identify the unknown and assign a variable to it.
Translate the words into an algebraic expression.
Set up the equation based on the given information.

Here鈥檚 how it works for our example:

We identified our unknown number and called it x.
'Three times the number' translates to the algebraic expression 3x.
We know that 'three times the number is 348', so we write the equation:
3x = 348

Now, our word problem is represented as an equation. This provides a clear path towards finding the solution.

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91影视

Translate each problem to an equation. Do not solve. Three times what number is \(348 ?\)

Short Answer

Step by step solution

Identify the unknown number

Express 'three times the number'

Set up the equation

Key Concepts

algebraic expressions

variables

setting up equations

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