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

Question

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?

Video Solution

Solution Steps

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 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 becauseitis30because it is 30% higher.</p></li><li><p>Form the equation based on the total cost:</p></li></ul><p>Equation:</p><p><span class="katex">\( 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 \times 8 = 10.4

    The price of the notebook is 10.4.</p><p>Therefore,thesolutiontotheproblemis:<strong>Notebook10.4.</p><p>Therefore, the solution to the problem is: <strong>Notebook 10.4, pen 8$.

Answer

Notebook 10.4 ,pen8, pen 8