3) Our school's art teacher took his class to a concert hall and paid $512 for 10 adult tickets and 9 children tickets. The next day, our music teacher took our class to the same concert hall and paid a total of $831 for 17 children and 15 adults. If a represents the price of an adult ticket, and c represents the price of a child's ticket, which system of equations can be used to find how much each child ticket and each adult ticket cost? A) 19ac-512 32ac-831 B) 10+9512 154+17c-83 10c+9a-512 15c+17a-83 D) 19(a+c)=512 32(a+c)-83
3) Our school's art teacher took his class to a concert hall and paid $512 for 10 adult tickets and 9 children tickets. The next day, our music teacher took our class to the same concert hall and paid a total of $831 for 17 children and 15 adults. If a represents the price of an adult ticket, and c represents the price of a child's ticket, which system of equations can be used to find how much each child ticket and each adult ticket cost? A) 19ac-512 32ac-831 B) 10+9512 154+17c-83 10c+9a-512 15c+17a-83 D) 19(a+c)=512 32(a+c)-83
Chapter11: Conics
Section11.5: Solve Systems Of Nonlinear Equations
Problem 241E: Explain in your own words how to solve a system of equations using substitution.
Related questions
Question
![**Problem 3 Explanation:**
Our school's art teacher took his class to a concert hall and paid $512 for 10 adult tickets and 9 children tickets. The next day, our music teacher took our class to the same concert hall and paid a total of $831 for 17 children and 15 adults.
If \( a \) represents the price of an adult ticket, and \( c \) represents the price of a child's ticket, which system of equations can be used to find how much each child ticket and each adult ticket cost?
**Options:**
A)
\[
\begin{align*}
19c + a &= 512 \\
32ac &= 831 \\
\end{align*}
\]
B)
\[
\begin{align*}
10a + 9c &= 512 \\
15a + 17c &= 831 \\
\end{align*}
\]
C)
\[
\begin{align*}
10c + 9a &= 512 \\
15c + 17a &= 831 \\
\end{align*}
\]
D)
\[
\begin{align*}
19(a + c) &= 512 \\
32(a + c) &= 831 \\
\end{align*}
\]
On an educational website, use these details to explain the problem context and guide users in understanding which option correctly represents the system of equations, keeping in mind the number of tickets and total amounts paid for each trip.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c097a51-27d3-4444-b37f-ca23cae8deb2%2Fd5c22e2e-7aec-45c3-a0b5-4e7fe6682958%2F52crmgl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 3 Explanation:**
Our school's art teacher took his class to a concert hall and paid $512 for 10 adult tickets and 9 children tickets. The next day, our music teacher took our class to the same concert hall and paid a total of $831 for 17 children and 15 adults.
If \( a \) represents the price of an adult ticket, and \( c \) represents the price of a child's ticket, which system of equations can be used to find how much each child ticket and each adult ticket cost?
**Options:**
A)
\[
\begin{align*}
19c + a &= 512 \\
32ac &= 831 \\
\end{align*}
\]
B)
\[
\begin{align*}
10a + 9c &= 512 \\
15a + 17c &= 831 \\
\end{align*}
\]
C)
\[
\begin{align*}
10c + 9a &= 512 \\
15c + 17a &= 831 \\
\end{align*}
\]
D)
\[
\begin{align*}
19(a + c) &= 512 \\
32(a + c) &= 831 \\
\end{align*}
\]
On an educational website, use these details to explain the problem context and guide users in understanding which option correctly represents the system of equations, keeping in mind the number of tickets and total amounts paid for each trip.
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