Question

How do you create and solve equations in one variable given a real-world situation?

Answer 1

@imqwerty

Answer 2

@quickstudent

Answer 3

This is an important skill, especially when you have a real world job about CS, Economics, Engineering (and a ton of other stuff). It's important that when you learn something in math, you know about its real world applications. A common example of this is derivatives/integrals and real world kinetics.

When you come across a real-world situation that needs to involve some sort of mathematics, you have to be able to identify what exactly is going on (what kind of change, what units are changing, etc.). You also have to be familiar with not just common Algebra and (single variable) Calculus, Trig, etc. formulas, but the concepts behind them and how they can be applied in the real world.

To solve them, you have to be familiar with algebraic, trigonometric etc. operations.

Answer 4

Generally speaking, you take the information you are given, and you assign the unknown a letter, called a variable. Then by carefully reading the problem, you do mathematical operations on the variable to reproduce what the problem tells you. There must be an equal sign in the expression since you need an equation. Then you solve the equation for the variable, and thus, you find out what the unknown, represented by the variable, equals. When you answer the question, answer it in words, not using the variable since the variable is something you used to solve the problem, not something you were told.

Answer 5

Here is an example.

Problem:
Mary has a bank account, but she does not remember how much money she has in it. She went to the bank, and she deposited $35. Then she asked for her account balance. She was told she has $63.25, including the $35 deposit. How much money did she have in her account before the $35 deposit?

Solution:
We are looking for the amount of money she had before the deposit. The unknown is this amount of money, so let's use a variable to represent the unknown amount.

We will use x as our variable.
Let x = amount of money in bank account before the $35 deposit

Now we need to see what the problem tells us happened to the unknown amount x, and we represent that with mathematical operations.

She deposited $35. That means the amount she had, x, was now increased by $35. Increasing this way means an addition of money.

That means she now has, in dollars, x + 35 in her bank account.

Now we read that the total she has after the deposit is $63.25.

She has x + 35, and she has 63.25, that means x + 35 must equal 63.25.
We now use the equal sign, and we have an equation:

x + 35 = 63.25

That is the equation that represents our problem. Now we solve the equation.

Subtract 35 from both sides:

x + 35 = 63.25
- 35 -35
--------------
x = 28.25

The solution to our equation is x = 28.25.

We do not give that solution as it is as the answer to the problem. The problem did not mention x. We used x as a tool to solve the problem. We must answer the question in a way that makes sense. Since x represents the amount of money Mary had in the account before the $35 deposit, and that is exactly what the question is asking, we answer:

Mary had $28.25 in the account before the $35 deposit.