Mark the Variable

The problem is asking how much the book without a cover costs so we mark that as our variable.

X = how much does the book without a cover costs.

Now, we will make the connection between the variable and the key data.

Book without the cover: X

The cover: 20% of X

We write our problem in form of an equation.

$\displaystyle x+\frac{20}{100}x=24$

$\displaystyle x+\frac{1}{5}x=24$

We use the multiplication axiom to get rid of the fraction.

$\displaystyle 5x+5\frac{1}{5}x=24$

$\displaystyle 5x+5\frac{1}{5}x=5\cdot 24$

$\displaystyle 5x+x=120$

$\displaystyle 6x=120$

$\displaystyle x=\frac{120}{6}$

x = 20

The answer: The book without a cover costs 20 dollars.

The proof:

The cover costs 20% of 20 dollars = 4 dollars.

20 dollars + 4 dollars = 24 dollars that costs the book.

See also: Quadratic equation