Henry sold a bicycle at 8% gain. Had it been sold for $ 75 more the gain would have been 14%. Find the cost of the bicycle.

Answer

To find the cost of the bicycle that Henry sold, we can follow these steps:

### Step 1: Define the Variables
Let the cost price (CP) of the bicycle be \( x \).

### Step 2: Calculate Selling Price for 8% Gain
If Henry sold the bicycle at an 8% gain, the selling price (SP) can be calculated as:
\[ SP_1 = CP + 8\% \text{ of } CP = x + 0.08x = 1.08x \]

### Step 3: Calculate Selling Price for 14% Gain
If the bicycle was sold for $75 more, the selling price would also yield a 14% gain:
\[ SP_2 = CP + 14\% \text{ of } CP = x + 0.14x = 1.14x \]
Since this selling price is $75 more than the first selling price, we can write:
\[ SP_2 = SP_1 + 75 \]
Substituting the expressions for \( SP_1 \) and \( SP_2 \):
\[ 1.14x = 1.08x + 75 \]

### Step 4: Solve for x
Now, we can solve for \( x \):
\[ 1.14x - 1.08x = 75 \]
\[ 0.06x = 75 \]
\[ x = \frac{75}{0.06} = 1250 \]

### Conclusion
The cost price of the bicycle is \( \text{CP} = 1250 \) dollars.

---