11 Beach Bicycles sells two-seater bicycles. Is markup rate is \( 65 \% \) which equation repreants the mew price for a bicycle, \( x \). given an original price, \( x \) ?

To determine the equation that represents the new price of a bicycle after applying a **65% markup** to the original price, let's define the variables clearly: - **Let \( P \) be the original price** of the bicycle. - **Let \( x \) be the new price** after the markup. ### Understanding Markup A **markup of 65%** means that the new price is **65% higher** than the original price. Mathematically, this can be expressed as: \[ \text{New Price} = \text{Original Price} + (0.65 \times \text{Original Price}) \] ### Formulating the Equation Substituting the variables: \[ x = P + 0.65P \] This can be simplified by factoring out \( P \): \[ x = P(1 + 0.65) \] \[ x = 1.65P \] ### Final Equation Therefore, the equation representing the new price \( x \) in terms of the original price \( P \) is: \[ x = 1.65 \times P \] ### Example If the original price \( P \) is \$200: \[ x = 1.65 \times 200 = \$330 \] So, the new price after a 65% markup would be \$330. **Summary:** \[ \boxed{x = 1.65 \times \text{(original price)}} \] This equation shows that the new price \( x \) is **165%** of the original price, accounting for the 65% markup.