Question

estimation the manager of a store increases the price of a popular product by 8%. let z be the original price of the product. the new price is z + 0.08z. write an equivalent expression by combining like terms. if the original price was $15.99, estimate the new price by first rounding the original price to the nearest dollar. find an expression equivalent to z + 0.08z. choose the correct expression below. a. 0.08z b. 0.02z c. 1.02z d. 1.08z

Explanation:

Step1: Identify like terms

The expression is \( z + 0.08z \). Here, \( z \) can be written as \( 1z \) (since any number multiplied by 1 is itself). So the terms \( 1z \) and \( 0.08z \) are like terms (both have the variable \( z \)).

Step2: Combine like terms

To combine like terms, we add their coefficients. The coefficient of \( z \) in \( 1z \) is 1, and the coefficient of \( z \) in \( 0.08z \) is 0.08. So we add \( 1 + 0.08 \).
\( 1 + 0.08 = 1.08 \).
Therefore, \( z + 0.08z = (1 + 0.08)z = 1.08z \).

Answer:

D. \( 1.08z \)