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Ms. Chapman wants to take her scout troop to Neon Nights roller rink. The employee she spoke to ahead of time said the total cost for all 99 people in the group would be $81\$81. This includes an entrance ticket and a $3\$3 skate rental fee for each person.\newlineWhich equation can you use to find tt, the cost of each entrance ticket?\newlineChoices:\newline(A) 9(t+3)=819(t + 3) = 81\newline(B) 3(t+9)=813(t + 9) = 81\newline(C) 3t+9=813t + 9 = 81\newline(D) 9t+3=819t + 3 = 81\newlineHow much does each entrance ticket cost?\newline____ $\$

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Q. Ms. Chapman wants to take her scout troop to Neon Nights roller rink. The employee she spoke to ahead of time said the total cost for all 99 people in the group would be $81\$81. This includes an entrance ticket and a $3\$3 skate rental fee for each person.\newlineWhich equation can you use to find tt, the cost of each entrance ticket?\newlineChoices:\newline(A) 9(t+3)=819(t + 3) = 81\newline(B) 3(t+9)=813(t + 9) = 81\newline(C) 3t+9=813t + 9 = 81\newline(D) 9t+3=819t + 3 = 81\newlineHow much does each entrance ticket cost?\newline____ $\$
  1. Identify Cost Components: Identify the total cost and components of the cost for each person. Each person pays for an entrance ticket tt and a skate rental fee of 3$3\$. The total cost for 99 people is 81$81\$.
  2. Set Up Equation: Set up the equation to represent the total cost.\newlineThe total cost for one person is the ticket price plus the skate rental, so for one person it's t+3t + 3 $\$. For 99 people, it would be 99 times (t+3(t + 3 $\$), which gives the equation 9(t+3)=819(t + 3) = 81.
  3. Solve for t: Solve the equation for t.\newlineFirst, divide both sides of the equation by 99 to isolate the term with tt:\newline9(t+3)=819(t + 3) = 81\newline(t+3)=819(t + 3) = \frac{81}{9}\newlinet+3=9t + 3 = 9\newlineNext, subtract 33 from both sides to solve for tt:\newlinet+33=93t + 3 - 3 = 9 - 3\newlinet=6t = 6