- Define the markup as a decimal: \(28\% = 0.28\).
- Set up the equation for the new price: \(y = x + 0.28x\).
- Simplify the expression: \(y = (1 + 0.28)x = 1.28x\).
- The correct equation is \(\boxed{y = 1.28x}\), which matches option (B).
Explanation
- Analyzing the Pricing Model
To determine the equation for the new price \(y\) after a markup of 28% on an original price \(x\), we first identify the components of the pricing model. The original price is represented by \(x\). A markup of 28% means that the increase in price is 28% of the original price, which can be expressed in decimal form as \(0.28x\). The new price \(y\) is then the sum of the original price and the markup: \(y = x + 0.28x\).
- Simplifying the Expression
We can simplify the expression \(y = x + 0.28x\) by factoring out the common variable \(x\). This gives us \(y = (1 + 0.28)x\). Performing the addition inside the parentheses results in \(y = 1.28x\). This equation represents the total price as 128% of the original price, accounting for the 100% initial value plus the 28% increase.
- Conclusion and Selection of the Correct Option
Comparing our derived equation \(y = 1.28x\) to the given options:
A\(y = 0.72x\)
B\(y = 1.28x\)
C\(y = x - 0.72\)
D\(y = x + 1.28\)
The equation \(y = 1.28x\) matches option (B). Therefore, the new price of the bag of dog food is correctly represented by the equation \(y = 1.28x\).
Examples
Understanding markups is essential in retail and business management. For example, if a store buys a product for \(\$50\) and wants to apply a 28% markup to cover overhead costs and generate profit, they would calculate the selling price as \(\$50 \times 1.28 = \boxed{\$64}\). This demonstrates how algebraic expressions directly apply to pricing strategies and financial planning.