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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.Two 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. Randolph purchased child tickets and adult tickets, which cost a total of . Mr. Kent purchased adult ticket, paying a total of . What are the ticket prices?The price of a child ticket is and the price of an adult ticket is .
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Q. Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.Two 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. Randolph purchased child tickets and adult tickets, which cost a total of . Mr. Kent purchased adult ticket, paying a total of . What are the ticket prices?The price of a child ticket is and the price of an adult ticket is .
- Define Variables: Let be the price of a child ticket and be the price of an adult ticket.Mrs. Randolph's purchase: Mr. Kent's purchase:
- Create Augmented Matrix: Write the system of equations as an augmented matrix:\begin{array}{cc|c} 30 & 23 & 1359 \ 1 & 1 & 33 \end{array}
- Transform to Row-Echelon Form: Use row operations to transform the matrix into row-echelon form.First, swap the rows so the smaller coefficient of is in the top row.\begin{align*}\(\newline&\begin{array}{cc|c}1 & 1 & 33 (\newline\)30 & 23 & 1359\end{array}\end{align*}\)
- Eliminate Variable : Multiply the first row by and add it to the second row to eliminate from the second row.This results in the new second row:
- Solve for Variable : Divide the second row by to solve for .This gives us , which is incorrect because ticket prices can't be negative.
