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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineTwo fifth grade classes are attending an amusement park as a field trip. Their teachers purchased the tickets for the class and the parent chaperones. Mrs. Arnold purchased 2323 child tickets and 11 adult ticket, which cost a total of $280\$280. Mr. Norton purchased 2525 child tickets and 2626 adult tickets, paying a total of $977\$977. What are the ticket prices?\newlineThe price of a child ticket is _____ and the price of an adult ticket is $\$_____.

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Solve a system of equations using elimination: word problemsright chevron icon

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineTwo fifth grade classes are attending an amusement park as a field trip. Their teachers purchased the tickets for the class and the parent chaperones. Mrs. Arnold purchased 2323 child tickets and 11 adult ticket, which cost a total of $280\$280. Mr. Norton purchased 2525 child tickets and 2626 adult tickets, paying a total of $977\$977. What are the ticket prices?\newlineThe price of a child ticket is _____ and the price of an adult ticket is $\$_____.
  1. Write Equations: Write the equations based on the given information.\newlineMrs. Arnold's purchase: 2323 child tickets and 11 adult ticket for $280\$280.\newlineMr. Norton's purchase: 2525 child tickets and 2626 adult tickets for $977\$977.\newlineLet xx be the price of a child ticket and yy be the price of an adult ticket.\newlineEquation for Mrs. Arnold's purchase: 23x+1y=28023x + 1y = 280\newlineEquation for Mr. Norton's purchase: 25x+26y=97725x + 26y = 977
  2. Set Up System: Set up the system of equations.\newlineWe have the following system:\newline23x+y=28023x + y = 280\newline25x+26y=97725x + 26y = 977
  3. Eliminate Variable: Decide which variable to eliminate.\newlineWe can multiply the first equation by −26-26 to eliminate yy when we add the equations together.
  4. Multiply and Write: Multiply the first equation by −26-26 and write the new system.\newline−26(23x+y)=−26(280)-26(23x + y) = -26(280)\newline25x+26y=97725x + 26y = 977\newlineThis gives us:\newline−598x−26y=−7280-598x - 26y = -7280\newline25x+26y=97725x + 26y = 977
  5. Add Equations: Add the two equations to eliminate yy.(−598x−26y)+(25x+26y)=−7280+977(-598x - 26y) + (25x + 26y) = -7280 + 977−598x+25x=−7280+977-598x + 25x = -7280 + 977−573x=−6303-573x = -6303
  6. Solve for x: Solve for x.\newlineDivide both sides by −573-573 to find the value of x.\newlinex=−6303−573x = \frac{-6303}{-573}\newlinex=11x = 11
  7. Substitute and Solve: Substitute xx back into one of the original equations to solve for yy. Using the first equation: 23x+y=28023x + y = 280 23(11)+y=28023(11) + y = 280 253+y=280253 + y = 280 y=280−253y = 280 - 253 y=27y = 27
  8. Write Final Answer: Write the final answer.\newlineThe price of a child ticket is $11\$11 and the price of an adult ticket is $27\$27.

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