Problem 64 - Elementary and Intermediate Algebra

Question

Translate each problem to an equation. Do not solve. What number added to 73 is \(201 ?\)

Step-by-Step Solution

Answer

The equation is + 73 = 201.

Step 1 - Identify what is unknown

Determine what the problem is asking you to find. In this case, it is asking for a number that when added to 73 equals 201.

Step 2 - Let a variable represent the unknown number

Let's use the variable to represent the unknown number that we are trying to find.

Step 3 - Translate the problem into an equation

According to the problem, adding the unknown number to 73 results in 201. This relationship can be written as the equation: + 73 = 201.

Key Concepts

Unknown Variable

When faced with a problem in algebra, the first step is to identify the unknown value you need to find. In this exercise, we are asked 'What number added to 73 is 201?' The unknown number here is what we need to determine. In algebra, we represent unknown values using variables, usually letters like \( x \) or \( n \). This helps to set up the equation we need to solve. Imagine a locked treasure box. The unknown number is like the key to this box. Without the variable representing it, we can't even begin to find the solution.

Equation Formation

After identifying the unknown variable, our next step is to form an equation that represents the problem. An equation is a mathematical statement that shows the relationship between different values. In algebra, it usually includes an equals sign (\(=\)). Let's take the problem again: What number (unknown variable) added to 73 equals 201? We can represent this unknown number by a variable, say \( x \).
Now we form the equation: \(+ 73 = 201 \)
This equation tells us that when we add our unknown variable \( x \) to 73, the sum equals 201. Creating the right equation is crucial because it provides a clear and manipulable representation of the problem. Think of it like a recipe; all ingredients need to be listed for the final dish (solution) to turn out right.

Addition in Algebra

Addition in algebra works similarly to regular addition, but with the inclusion of variables. When the problem states, 'What number added to 73 is 201?', it invites us to use algebraic addition.
Here, we set up our equation: \( x + 73 = 201 \). In this equation, \[ 73 \] is a known number, and \( x \) is the unknown variable. Addition in algebra allows us to combine known and unknown values to form meaningful equations, which we can solve to find the value of the unknown variable.
By engaging with such problems, students learn that algebraic addition is a powerful tool for solving real-world problems and mathematical queries. Understanding how to translate verbal problems into equations and manipulate these equations is key to mastering algebra.