Bernard's Dining Dilemma: How Much is Each Coupon Worth?

To solve this problem, we'll proceed with the following steps:

• Step 1: Define the variable for the value of a coupon: Let $x$ be the worth of one coupon.
• Step 2: Formulate the equation based on the given condition: Since 12 coupons cover both the 200 and 8 coupons, the equation is \( 12x = 200 + 8x .
• Step 3: Solve the equation for $x$:
  $12x = 200 + 8x$
  Subtract $8x$ from both sides:
  $12x - 8x = 200$
  Simplify:
  $4x = 200$
• Step 4: Solve for $x$:
  Divide both sides by 4:
  $x = \frac{200}{4} = 50$

Thus, each coupon is worth \50 \).