Solve for Pen Price: 4 Pens + 9 Notebooks = $51 with Double Price Relationship

Daniela goes to the bookshop and buys 4 pens and 9 notebooks for a total of $51.

The price of a pen is twice as much as the price of a notebook.

How much is a pen?

We will identify the price of the notebook with x and since the price of the pen is 2 times greater we will mark the price of the pen with 2x

The resulting equation is 4 times the price of a pen plus 9 times the price of a notebook = 51

Now we replace and obtain the following equation:

\( 4\times2x+9\times x=51

According to the rules of the order of arithmetic operations, multiplication and division operations precede addition and subtraction, therefore we will first solve the two multiplication exercises and then add them up:

$(4\times2x)+(9\times x)=51$

$(4\times2x)=8x$

$(9\times x)=9x$

$8x+9x=17x$

Now the obtained equation is: $17x=51$

We divide both sides by 17 and find x

$x=\frac{51}{17}=3$

As we discovered that x is equal to 3, we will place it accordingly and find out the price of a pen:$2\times x=2\times3=6$