Question

Mrs. Brady purchased an item on sale and described her purchase to her students. Four students each wrote an expression to represent the cash Mrs. Brady paid for the item, in dollars, given an original

price of P and the use of a five dollar gift card to help pay for the purchase. Their expressions are shown in the table below.
Student Expression
Jacob LaTeX: -5+P-0.25P− 5 + P − 0.25 P
Rylee LaTeX: 0.75P-50.75 P − 5
Tamar LaTeX: P-\frac{25}{100}P-5P − 25 100 P − 5
Marta LaTeX: -5+\frac{3}{4}P− 5 + 3 4 P
Which statements about the expressions provided by the students are true?

A) The expressions with more terms indicate a different sale price than the expressions with fewer terms.
B) The constant term in each expression indicates the original price of the item Mrs. Brady purchased.
C) The constant term in each expression indicates that the sale price is not dependent on the original price of the item.
D) The constant term in each expression indicates the amount deducted when the gift card was applied to the purchase.
E) The variable terms in all four expressions indicate that the item was on sale for 25 percent off.

Answer 1

True statements regarding the expressions provided by the students for Mrs. Brady's purchase include that the constant term in each expression indicates the amount deducted by the gift card, and the variable terms indicate a 25% discount on the original price.

Step-by-step explanation:

When assessing the expressions provided by the students representing Mrs. Brady's purchase, we must consider both the constant and the variable terms. The original price of the item is denoted as P, and a gift card valued at $5 is used towards the purchase.

Let's evaluate the provided statements:

• A) Incorrect. More terms in an expression do not necessarily indicate a different sale price; they may just represent the calculation differently.
• B) Incorrect. The constant term in each expression is -5, indicating the value of the gift card used, not the original price of the item.
• C) Incorrect. The constant term indicates the deduction of the gift card, and is dependent on the original price since it reduces the amount paid.
• D) Correct. The constant term -5 in each expression signifies the $5 gift card applied to the purchase.
• E) Correct. The variable terms in all four expressions indeed indicate a 25% discount on the item's original price P, which is equivalent to 0.75P.