Question

mal works at a photo gallery. he charges $50 for a large photo and $40 for a large frame. sales tax is 5%. how much total tax will a customer pay on both? fill in the blanks to show how to write and simplify expressions that represent the problem. 3 of 4 questions one way to calculate the total tax is 0.05(50 + 40). the total tax is $ select... expand the expression 0.05(50 + 40) using the distributive property. the new expression is select... the total tax using the new expression is select... the tax calculated using the original expression.

Explanation:

First Blank (Total Tax Amount)

Step1: Calculate inside the parentheses

First, add the cost of the photo and the frame: \( 50 + 40 = 90 \)

Step2: Multiply by the tax rate

Then, multiply the sum by the tax rate (0.05): \( 0.05 \times 90 = 4.5 \)

Step1: Apply the distributive property

The distributive property states that \( a(b + c) = ab + ac \). Here, \( a = 0.05 \), \( b = 50 \), and \( c = 40 \). So, \( 0.05(50 + 40) = 0.05 \times 50 + 0.05 \times 40 \)

Step2: Simplify each term (optional for expression)

Calculating each term: \( 0.05 \times 50 = 2.5 \) and \( 0.05 \times 40 = 2 \), but the expanded expression is \( 0.05 \times 50 + 0.05 \times 40 \) (or simplified as \( 2.5 + 2 \), but the expanded form from distribution is \( 0.05(50) + 0.05(40) \))

Step1: Recall the distributive property

The distributive property ensures that \( a(b + c) = ab + ac \), so both expressions (original and expanded) should give the same result. We calculated the total tax as \( 4.5 \) using the original expression, and using the expanded expression: \( 2.5 + 2 = 4.5 \), which is the same.

Step2: Determine the relationship

Since both methods give the same tax amount, the total tax using the new expression is equal to the tax calculated using the original expression.

Answer:

\( 4.5 \)

Second Blank (Expanded Expression)