Question

1. maple grove middle school is selling spirit gear. sweatshirts, shorts, t - shirts, and sweatpants are available. each item purchased will have a 6% sales tax added to the cost. write an expression as a product to represent the total cost of all the items (c).

Explanation:

Step1: Define the cost before tax

Let the total cost of all items before tax be \( P \).

Step2: Calculate the tax factor

The sales tax is 6%, which is \( 0.06 \) in decimal form. The total cost including tax is the cost before tax plus the tax, which can be written as \( P + 0.06P \). Factoring out \( P \), we get \( P(1 + 0.06) \). Simplifying \( 1 + 0.06 \) gives \( 1.06 \). So the expression for the total cost \( C \) is \( C = 1.06P \), or as a product, if we consider the original cost of items as a sum (but since we need a product expression, and the tax is a multiplier on the pre - tax cost), the expression is \( C = 1.06\times P \) where \( P \) is the total cost of items before tax. If we let the cost of each item be, say, \( p_1,p_2,p_3,p_4 \) (for sweatshirts, shorts, t - shirts, sweatpants), then \( P=p_1 + p_2 + p_3 + p_4 \), and \( C = 1.06(p_1 + p_2 + p_3 + p_4) \), but as a product representing the total cost with tax, it's \( C=1.06\times(\text{total cost of items before tax}) \). A more general way, if we let \( x \) be the total cost of all items before tax, then the expression is \( C = 1.06x \) (where \( x \) is the sum of the costs of each item).

Answer:

If \( x \) is the total cost of all items before tax, the expression for the total cost \( C \) is \( C = 1.06x \) (or \( C=(1 + 0.06)x \))