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Math Asked by a SnapAndSolve user · about 2 hours ago

Adrian is working at the fair collecting money for tickets. Tickets cost $4 for adults and $1.50 for...

Adrian is working at the fair collecting money for tickets. Tickets cost $4 for adults and $1.50 for children. On Saturday, 2,200 people came to the fair and Adrian collected $5,050. How many adults and how many children came to the fair?
HINT: Write a system of equations for the situation. Solve the system to answer the problem.
- 1500 adults, and 700 kids
- 700 adults, and 1500 kids
- 100 adults, and 3100 kids
- 1000 adults, and 1200 kids

Answer

Let a be the number of adults and c be the number of children. We can set up the following system of equations based on the problem:

  1. Total people: a + c = 2200
  2. Total money collected: 4a + 1.5c = 5050

Solving the system:

  1. From the first equation, express a in terms of c: a = 2200 - c
  2. Substitute into the second equation: 4(2200 - c) + 1.5c = 5050
  3. Simplify: 8800 - 4c + 1.5c = 5050
  4. Combine like terms: 8800 - 2.5c = 5050
  5. Solve for c: 2.5c = 8800 - 5050 = 3750
  6. c = 1500
  7. Substitute back to find a: a = 2200 - 1500 = 700

Therefore, the answer is 700 adults, and 1500 kids.

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