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

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
00:00 Determine the price of a ruler a pen cost
00:04 Mark the price of the pen with unknown X
00:26 Determine from the given data how much the ruler costs and express it using X
00:39 Convert percentages to fractions and simplify wherever possible
00:43 Find a common denominator and combine
00:54 This is the expression for the ruler's price using X
01:06 Now let's write the equation for the price of the ruler and pen together
01:20 Convert the whole number to fractions
01:38 Isolate X by multiplying by the reciprocal fraction
01:56 Make sure to multiply numerator by numerator and denominator by denominator (1)
02:04 This is the price of the pen (X)
02:14 Insert this price into the expression for the ruler's price and proceed to solve
02:23 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

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?

2

Step-by-step solution

To find the individual prices of the notebook and pen:

  • Define the price of the pen as x x $.

  • The notebook price, therefore, will be 1.3x 1.3x $because it is 30% higher.

  • Form the equation based on the total cost:

Equation:

x+1.3x=18.4 x + 1.3x = 18.4

Combine like terms to simplify:

2.3x=18.4 2.3x = 18.4

To find x x , divide both sides by 2.3:

x=18.42.3 x = \frac{18.4}{2.3}

Calculate x x :

x=8 x = 8

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

1.3x=1.3×8=10.4 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$, pen 8$.

3

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 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 15% of 100:

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?

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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?

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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?

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

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

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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 1x + 1.3x = 2.3x .

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