Question

there are 12 paperback mysteries on a shelf. this is 40% of the books on the shelf. write and solve an equation to find the number of books on the shelf. show your work

Explanation:

Step1: Define the variable

Let \( x \) be the total number of books on the shelf.

Step2: Set up the equation

We know that 40% of the total books \( x \) is equal to the number of paperback mysteries, which is 12. So we can write the equation as \( 0.4x = 12 \) (since 40% is equivalent to 0.4 in decimal form).

Step3: Solve for \( x \)

To solve for \( x \), we divide both sides of the equation by 0.4. So \( x=\frac{12}{0.4} \).
Calculating \( \frac{12}{0.4} \), we can multiply the numerator and denominator by 10 to get rid of the decimal in the denominator: \( \frac{12\times10}{0.4\times10}=\frac{120}{4} = 30 \).

Answer:

The total number of books on the shelf is 30.