Math Problem Statement
The admission fee at an amusement park is $2.75 for children and $6.60 for adults. On a certain day, 303 people entered the park, and the admission fees collected totaled $1276. How many children and how many adults were admitted?
Solution
The problem can be solved by setting up a system of linear equations.
Let:
- be the number of children
- be the number of adults
We have two pieces of information:
- The total number of people is 303:
- The total amount of money collected is $1276. Since children pay $2.75 and adults pay $6.60, we can write:
Now, we have the system of equations:
x + y &= 303 \\ 2.75x + 6.60y &= 1276 \end{aligned}$$ ### Step 1: Solve the first equation for one variable. From the first equation, solve for $$y$$: $$y = 303 - x$$ ### Step 2: Substitute $$y$$ into the second equation. Substitute $$y = 303 - x$$ into the second equation: $$2.75x + 6.60(303 - x) = 1276$$ Now simplify and solve for $$x$$: $$2.75x + 6.60(303) - 6.60x = 1276$$ $$2.75x + 1999.8 - 6.60x = 1276$$ $$-3.85x + 1999.8 = 1276$$ $$-3.85x = 1276 - 1999.8$$ $$-3.85x = -723.8$$ $$x = \frac{-723.8}{-3.85} = 188$$ So, $$x = 188$$, meaning there are 188 children. ### Step 3: Find $$y$$. Substitute $$x = 188$$ back into the first equation: $$188 + y = 303$$ $$y = 303 - 188 = 115$$ So, there are 115 adults. ### Final answer: - Number of children = 188 - Number of adults = 115 Would you like further clarification or additional details? Here are some related questions to explore: 1. How would the solution change if the total admission fees collected were higher? 2. What if the adult fee was increased to $7.50? How would that affect the number of children and adults? 3. Can you solve the same problem using substitution or graphing methods? 4. What happens if the park introduces a family discount for a group of 4? 5. How would this system work if more types of tickets (like senior tickets) were added? **Tip:** Always check if the solution makes sense by plugging the values back into both original equations to ensure correctness!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Equations
Linear Equations
Formulas
x + y = 303
2.75x + 6.60y = 1276
Theorems
Solving Systems of Equations
Suitable Grade Level
Grades 8-10