Beach Bicycles sells two-seater bicycles. Its markup rate is $$ 68 \% $$. Which equation represents the new price for a bicycle, $$ y $$. given an original price, $$ x $$ ? (A) $$ y=0.32 x $$ (B) $$ y=x-0.32 $$ (C) $$ y=1.68 x $$ (4) $$ y=x+0.68 $$

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To determine the new price $$ y $$ of a bicycle after applying a markup rate of $$ 68\% $$ to the original price $$ x $$, we can use the following approach:

1. **Understanding Markup**:
   - A markup of $$ 68\% $$ means that the selling price is $$ 68\% $$ higher than the original price.
   - Mathematically, this can be expressed as:
     $$
     y = x + 0.68x
     $$
   - Simplifying the equation:
     $$
     y = 1.68x
     $$

2. **Matching with the Options**:
   - **Option (A)**: $$ y = 0.32x $$ — This represents a $$ 32\% $$ markup, which is incorrect.
   - **Option (B)**: $$ y = x - 0.32 $$ — This incorrectly subtracts a fixed amount rather than applying a percentage.
   - **Option (C)**: $$ y = 1.68x $$ — This correctly represents a $$ 68\% $$ markup.
   - **Option (D)**: $$ y = x + 0.68 $$ — This adds a fixed amount of $$ 0.68 $$ instead of $$ 68\% $$.

Therefore, the correct equation representing the new price with a $$ 68\% $$ markup is:

**Answer:**  
(C) $$ y = 1.68\,x $$
The correct equation is $$ y = 1.68x $$.

Beach Bicycles sells two-seater bicycles. Its markup rate is \( 68 \% \). Which equation represents the new price for a bicycle, \( y \). given an original price, \( x \) ? (A) \( y=0.32 x \) (B) \( y=x-0.32 \) (C) \( y=1.68 x \) (4) \( y=x+0.68 \)

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