A bookstore has a sale where the price of any paperback book is reduced by 4 dollars. If t… — ACT

A bookstore has a sale where the price of any paperback book is reduced by $4$ dollars. If the sale price of a paperback book is $12$ dollars, and its original price is $p$ dollars, which of the following equations can be used to find $p$ ?

$p - 4 = 12$ Answer
B
$p + 4 = 12$
C
$4 - p = 12$
D
$4p = 12$
E
$\frac{p}{4} = 12$

Answer

The equation

p - 4 = 12

The original price of the book is

p

dollars. Since the price is reduced by

4

dollars, we subtract

4

from

p

, which is written as

p - 4

. Since this resulting sale price is equal to

12

dollars, the correct equation representing the relationship is

p - 4 = 12

Step-by-Step Solution

Identify the variable and the mathematical values given in the scenario.

The original price is represented by the variable

p

. The price reduction is

4

dollars, and the final sale price is

12

dollars.

This sets up the translation of the word problem into algebraic terms.

Translate the phrase 'reduced by

4

dollars' into an algebraic expression.

A reduction of

4

dollars from the original price

p

is written as

p - 4

A reduction or discount represents subtraction from the starting amount.

Equate the expression representing the sale price to the given sale price value.

The equation is

p - 4 = 12

Since the sale price is given as

12

dollars, the expression for the reduced price must equal

12

Key Concept

Translating real-world discount scenarios into one-step linear equations.

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic