Solve the Cost Equation: Notebook Price at 30% More Than Pen

Q: Why do we use 1.3x instead of x + 30%?

Because 30% more means 100% of the original price PLUS 30% more. So 100% + 30% = 130% = 1.3 times the original price. Writing x + 0.3 would only add 30 cents!

Q: How do I know which item to call x?

Always let x represent the smaller or simpler value. Since the notebook costs more than the pen, let the pen = x. This makes the math easier!

Q: Can I solve this by guessing and checking?

You could try, but algebra is much faster and more reliable. Setting up the equation $ x + 1.3x = 18.4 $ gives you the exact answer in just a few steps!

Linear Equations with Percentage Relationships

The price of a notebook is 30% higher than the price of a pen.

If together a notebook and a pen cost 18.4 $:
How much is the notebook and how much is the pen?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:12 Let's find out how much a ruler and a pen cost.

00:16 We'll start by calling the price of the pen X. Write down X for the cost of the pen.

00:38 Next, we'll use the information given to find how much the ruler costs. Express the ruler's price using X.

00:51 Now, change percentages to fractions and simplify them if you can.

00:57 Find a common bottom number, or denominator, for the fractions, and then combine them.

01:06 Great! This is the ruler's price expressed with X. Keep this in mind.

01:18 Let's set up an equation for the total price of the ruler and pen together.

01:32 Convert any whole numbers to fractions to make it easier to work with.

01:50 To solve for X, multiply by the reverse fraction, also known as the reciprocal.

02:08 Multiply the top numbers together, and do the same for the bottom numbers.

02:16 Nice job! This gives us the price of the pen, which is X.

02:26 Now plug this value of X into the expression for the ruler and let's solve it.

02:35 Awesome! And there's your solution. That's how you find the cost.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The price of a notebook is 30% higher than the price of a pen.

If together a notebook and a pen cost 18.4 $:
How much is the notebook and how much is the pen?

Step-by-step solution

To find the individual prices of the notebook and pen:

Define the price of the pen as $x$ $.
The notebook price, therefore, will be $1.3x$ $because it is 30% higher.
Form the equation based on the total cost:

Equation:

$x + 1.3x = 18.4$

Combine like terms to simplify:

$2.3x = 18.4$

To find $x$ , divide both sides by 2.3:

$x = \frac{18.4}{2.3}$

Calculate $x$ :

$x = 8$

Thus, the price of the pen is 8$. Now calculate the price of the notebook:

$1.3x = 1.3 \times 8 = 10.4$

The price of the notebook is 10.4$.

Therefore, the solution to the problem is: Notebook 10.4$, pen 8$.

Final Answer

Notebook 10.4 $, pen 8 $

Key Points to Remember

Essential concepts to master this topic

Variable Definition: Let the smaller value be x to simplify calculations
Percentage Formula: 30% more means multiply by 1.3, so notebook = $1.3x$
Verification: Check that pen + notebook = 8 + 10.4 = 18.4 ✓

Common Mistakes

Avoid these frequent errors

Adding 30% as 0.3 instead of multiplying by 1.3
Don't write notebook = x + 0.3 = wrong relationship! This treats 30% as 30 cents instead of 30% of the pen's price. Always use notebook = 1.3x to show 30% more than the pen's full price.

Practice Quiz

Test your knowledge with interactive questions

Calculate 30 over 100 as a percentage:

FAQ

Everything you need to know about this question

Why do we use 1.3x instead of x + 30%?

Because 30% more means 100% of the original price PLUS 30% more. So 100% + 30% = 130% = 1.3 times the original price. Writing x + 0.3 would only add 30 cents!

How do I know which item to call x?

Always let x represent the smaller or simpler value. Since the notebook costs more than the pen, let the pen = x. This makes the math easier!

What if I get a decimal answer like 8.0?

Decimal answers are completely normal in word problems! Just make sure to include the dollar sign and check that your decimals add up to the total cost given.

Can I solve this by guessing and checking?

You could try, but algebra is much faster and more reliable. Setting up the equation $x + 1.3x = 18.4$ gives you the exact answer in just a few steps!

Why do we combine x + 1.3x = 2.3x?

Because both terms have the same variable x! Think of it like: 1 apple + 1.3 apples = 2.3 apples. We're adding $1x + 1.3x = 2.3x$ .

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