Math Miscellaneous

4 Easy Steps To Solve Math Problem

I understand that most of the students struggle in solving any math problem. Don't worry, I'll share with you 4 easy steps that can help you to solve any math problem easily.

📗Polya's Method
Quick Background: George Polya is known as the Father of Modern Problem Solving and he devised a method to help you solve math problems.

Here are the steps:

🔖1. Understand the problem. Look for what is being asked in the problem. Don't confuse your mind with the other details in the problem. Focus on what you are going to find or solve.

🔖2. Devise a plan. Get the given figures (numbers, units, etc.) written in the problem and construct mathematical expression. If you are already familiar with translating phrases into mathematical expression, then you are good to go. But if you don't, worry not because I will provide an example below.

🔖 Carry out the plan. Solve the equation that you constructed during devising a plan.

🔖 Look back. Check your work if you don't miss important details like the positive or negative sign of a number. Always double check your answer if you think you missed something. It would be a waste of points if you rush your work but the answer is incorrect.

Easy guidelines right?

To help you understand better the method of Polya, here is the application.

🤔 The carpenter would like to build a fence around the house. The owner of the house requested that the length should be 4 meters longer than twice its width. The perimeter around the house is 100 meters. Find the length and the width.

✏️Step 1. Understand the problem.
📖To find the the length and the width.
✏️Step 2. Devise a plan. This is the time when you translate phrases into mathematical expression.

Let w be the width.
Translate this, "the length is 4 meters longer than twice its width".

It's quite confusing to translate the long phrase, so break it down first:
"the length is 4 meters longer than"✂️(cut), "twice its width"

Now translate the shorter phrase first:
"twice its width", it means that double the width or multiply the width by 2.
2 × w = 2w

Then, for the longer phrase:
"the length is 4 meters longer than"
Remember that it is 4 meters longer than (twice its width which is 2w), so:
write the length as: 2w + 4

Now, the length is 2w+4 and the width is w.

Remember that the formula for the perimeter of a rectangle is:
Perimeter = 2 × length + 2 × width

Substitute the length, the width, and the value of the perimeter into the formula, it follows:
100 = 2 × (2w+4) + 2 × w

Now, you have done the "devising a plan" part.

✏️Step 3. Carry out the plan. Solve the equation that you constructed.
100 = 2 × (2w+4) + 2 × w

Multiply 2 by (2w+4) and 2 by w on the right side of the equation:
100 = 4w+8 + 2w

Add like terms or the terms with the same variable w:
100 = 6w + 8

Add -8 on both sides of the equation to cancel out positive 8 on the right side:
100 - 8 = 6w + 8 - 8

Perform subtraction on both sides of the equation:
92 = 6w

Divide both sides by 6 to cancel out 6 on the right side of the equation:
92÷6 = 6w÷6

Perform division on both sides of the equation:
15.33 = w. ➡️ the value of width

Find the length by substituting the value of w into the length, 2w+4:
2×15.33 + 4

Compute:
34.66 ➡️ the value of length

📖 So, the length is 34.66 meters and the width is 15.33 meters.

✏️Step 4. Look back. Substitute the value of length and width into the formula of the perimeter and verify if the answer is correct:
Perimeter = 2 × length + 2 × width
100 = 2 × 34.66 + 2 × 15.33
100 = 69.32 + 30.66
100 = 99.98
Round up the right side of the equation:
100 = 100 ✔️

Therefore, from the solution down to to your final answer, you solved it correctly. Congratulations!

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I hope you like it and you have learned from it. I believe you can now solve any math problem like this.

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🤔If you have any question or clarification, feel free to write on the comment section below👇.

Have a nice day!🤗
-Your Math Assistant