Question

To participate in a bowling league, you pay a $25 sign up fee and $12 for each league night that you bowl. So, the total cost C (in dollars) is given by the equation
C=12x+25 where x is the number of league nights you bowl.
Solve for x:
How many league nights have you bowled if you spent a total of $145?
How many league nights have you bowled if you spent a total of $205?

Answer 1

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:

1. Set \( C = 145 \):

\[
145 = 12x + 25
\]

2. Subtract 25 from both sides:

\[
145 - 25 = 12x
\]

\[
120 = 12x
\]

3. 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:

1. Set \( C = 205 \):

\[
205 = 12x + 25
\]

2. Subtract 25 from both sides:

\[
205 - 25 = 12x
\]

\[
180 = 12x
\]

3. 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**.