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A store sells four-packs of permanent markers in assorted colors for $\$3.19$ per pack. All spiral-bound notebooks, whether wide-ruled or college-ruled, sell for $\$1.20$ each. Cleo buys $x$ packs of markers, $y$ wide-ruled notebooks, and $z$ college-ruled notebooks. The store charges a 6% sales tax on Cleo's total bill. Which expression represents the amount Cleo must pay after taxes?


A$3.19x + 1.20y + 1.20z + 1.06$
B$3.19x + 1.20yz + 1.06$
C$1.06(3.19x + 1.20yz)$
D$1.06(3.19x + 1.20y + 1.20z)$

Verified Answer :

  • Calculate the total pre-tax cost by summing the costs of individual items: \(3.19x + 1.20y + 1.20z\).
  • Apply a 6% sales tax by multiplying the pre-tax total by \(1.06\).
  • The resulting expression is \(1.06(3.19x + 1.20y + 1.20z)\).
  • Final Answer: \(\boxed{1.06(3.19x + 1.20y + 1.20z)}\)

Explanation

  1. Analyzing the Problem and Determining the Total Cost

The problem asks for an expression representing the total cost of Cleo's purchases after a 6% sales tax is applied.
We are given:

  • The price of a pack of permanent markers is \(\$3.19\).
  • The price of any spiral-bound notebook (wide-ruled or college-ruled) is \(\$1.20\).
  • Cleo buys \(x\) packs of markers, \(y\) wide-ruled notebooks, and \(z\) college-ruled notebooks.
  • A 6% sales tax is applied to the total pre-tax amount.

First, we calculate the total pre-tax cost.
The cost of markers is \(\$3.19 \times x = 3.19x\).
The cost of all notebooks is \(\$1.20 \times y + \$1.20 \times z = 1.20y + 1.20z\).
So, the total pre-tax cost is \(3.19x + 1.20y + 1.20z\).

To apply a 6% sales tax, we multiply the total pre-tax cost by \(1 + 0.06 = 1.06\).
Therefore, the total cost after tax is \(1.06 \times (3.19x + 1.20y + 1.20z)\).

  1. Evaluating the Options

Comparing the expression \(1.06(3.19x + 1.20y + 1.20z)\) with the given options:

  1. \(3.19x + 1.20y + 1.20z + 1.06\) - This adds the tax amount (as a flat fee) rather than applying it as a multiplier.
  2. \(3.19x + 1.20yz + 1.06\) - This multiplies the number of notebooks and adds a flat fee.
  3. \(1.06(3.19x + 1.20yz)\) - This multiplies the number of notebooks instead of summing their individual costs.
  4. \(1.06(3.19x + 1.20y + 1.20z)\) - This correctly represents the total cost after applying a 6% tax to the pre-tax total.

The correct expression is the fourth one.

Examples

Understanding how to calculate totals with sales tax is essential for everyday shopping. If you buy several items, each with its own unit price, you sum their costs first and then apply the tax rate as a multiplier. For example, if you buy groceries and stationery at different prices, this method ensures you calculate the correct total bill, helping you manage your budget and verify receipts.

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