To find the number of league nights you've bowled for the total costs of $145 and $205, we can use the equation given:
\[ C = 12x + 25 \]
where \( C \) is the total cost and \( x \) is the number of league nights bowled.
For a total cost of $145:
- Set \( C = 145 \):
\[ 145 = 12x + 25 \]
- Subtract 25 from both sides:
\[ 145 - 25 = 12x \]
\[ 120 = 12x \]
- Divide both sides by 12:
\[ x = \frac{120}{12} \]
\[ x = 10 \]
So, if you spent a total of $145, you have bowled 10 league nights.
For a total cost of $205:
- Set \( C = 205 \):
\[ 205 = 12x + 25 \]
- Subtract 25 from both sides:
\[ 205 - 25 = 12x \]
\[ 180 = 12x \]
- Divide both sides by 12:
\[ x = \frac{180}{12} \]
\[ x = 15 \]
So, if you spent a total of $205, you have bowled 15 league nights.
Summary:
- For a total cost of $145, you bowled 10 league nights.
- For a total cost of $205, you bowled 15 league nights.