Terning a text based problem into a number based problem

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In summary, when faced with a text-based problem, it is helpful to break it down into a number-based problem by assigning variables and writing equations for each sentence. Taking it slow and being systematic can help to avoid mixing up variables and solve the problem accurately.
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Restless
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Turning a text based problem into a number based problem

I can solve these types of questions such as:

4(3x-5)=5x+2(x+15)

but when a question is worded something like:

"The second of three numbers is 1 less than the first. The third number is 5 less than the second. If the first number is twice as large as the third, find the three numbers."

There is just too much going on in that worded problem for me to be able to express it differently.

A simple question like:

"A can of beans weighs twice as much as a can of coke plus 2lbs"

This is simple, I can just say:

b = 2c + 2

But the questions in my book are just so long winded -_- any tips?
 
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Just take it slow and be systematic. The first clue you are looking for is how many variables are there - which is three. Then you assign them names, eg. a, b and c. Then just write down the equations as they come along. For instance, the first sentence also tells you that b=a-1, and so on.
 
  • #3


Restless said:
The second of three numbers is 1 less than the first.
The third number is 5 less than the second.
If the first number is twice as large as the third,
find the three numbers.

You might want to choose names that you can't mix up part way through the problem.
First step might be this, to avoid using x for first and then later x for second or third.
Each sentence is turned directly into a single simple equation with appropriate names.

second= -1+first
third= -5+second
first= 2*third

Then if you need to the next step might be this

s=f-1
t=s-5
f=2*t

and solve that.

When you get something like s=4, t=2, f=5 you can look back at your original problem and see exactly what each of those results should be used for.

Just be careful to not mix up s and 5 or o and 0 or l and 1, etc.
 

FAQ: Terning a text based problem into a number based problem

1. How do you convert a text-based problem into a number-based problem?

To convert a text-based problem into a number-based problem, you first need to identify the key variables and numbers mentioned in the problem. Then, you can assign each variable a numerical value and use mathematical operations to solve the problem.

2. Why is it important to turn a text-based problem into a number-based problem?

Converting a text-based problem into a number-based problem allows for a more precise and objective solution. It also helps to eliminate any potential ambiguity or confusion that may arise from interpreting the problem in a purely textual form.

3. What are some common techniques for turning a text-based problem into a number-based problem?

Some common techniques for turning a text-based problem into a number-based problem include creating equations, using diagrams or graphs, and breaking the problem down into simpler parts that can be solved numerically.

4. Can a text-based problem always be converted into a number-based problem?

Yes, in most cases, a text-based problem can be converted into a number-based problem. However, there may be some problems that require qualitative or descriptive solutions, in which case it may not be necessary to convert the problem into a purely numerical form.

5. How can turning a text-based problem into a number-based problem benefit the problem-solving process?

Turning a text-based problem into a number-based problem can help to streamline the problem-solving process and make it more structured and organized. It can also make it easier to identify and understand the relationships between different variables and their impact on the overall solution.

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