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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?

1 answer

To solve for \( x \) in the equation \( C = 12x + 25 \), we can rearrange the equation to find the value of \( x \):

  1. Subtract the sign-up fee from the total cost: \[ C - 25 = 12x \]

  2. Divide both sides by 12: \[ x = \frac{C - 25}{12} \]

Now we can use this formula to find the number of league nights bowled for the given total costs.

Case 1: Total cost \( C = 145 \)

Substituting \( C = 145 \) into the equation: \[ x = \frac{145 - 25}{12} = \frac{120}{12} = 10 \]

Thus, if you spent a total of $145, you have bowled 10 league nights.

Case 2: Total cost \( C = 205 \)

Substituting \( C = 205 \) into the equation: \[ x = \frac{205 - 25}{12} = \frac{180}{12} = 15 \]

Thus, if you spent a total of $205, you have bowled 15 league nights.