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2:20 PM Wed Feb 19 68\% funny valenti Home I Schoc quarter note drip murals - Quiz: System BigBlueButto kanawha.schoology.com 514 HS ALGEBRA II_3072_02000000: 16 Quiz: Systems of Equations (Remote Learning Day) Submissions Enabled Grade: N/A This test/quiz is accepting submissions until Wednesday, February 19, 2025 at 3:00 pm Question 3 of \( 6 \mid \) Page 3 of 6 Question 3 (1 point) 4. A movie theater sells two types of tickets: adult tickets for \( \$ 10 \) each and child tickets for \( \$ 6 \) each. If the total revenue from 50 tickets sold was \( \$ 420 \), how many child tickets were sold? A) 20 B) 30 C) 25 D) 15 a 20 b \( \quad 30 \) C \( \quad 25 \) d \( \quad 15 \) Next Page Once you click Next Page you will not be able to change your answer

Ask by Chen Davies. in the United States
Feb 19,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

20 child tickets were sold.

Solution

To solve this problem, we can set up a system of equations based on the information given. Let's denote the number of adult tickets sold as \( A \) and the number of child tickets sold as \( C \). Given: - The total number of tickets sold is 50, so \( A + C = 50 \). - The total revenue from 50 tickets sold is $420, with adult tickets costing $10 each and child tickets costing $6 each. Therefore, the total revenue equation is \( 10A + 6C = 420 \). We can solve this system of equations to find the number of child tickets sold. Let's solve the system of equations using the substitution method. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}A+C=50\\10A+6C=420\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}A=50-C\\10A+6C=420\end{array}\right.\) - step2: Substitute the value of \(A:\) \(10\left(50-C\right)+6C=420\) - step3: Simplify: \(500-4C=420\) - step4: Move the constant to the right side: \(-4C=420-500\) - step5: Subtract the numbers: \(-4C=-80\) - step6: Change the signs: \(4C=80\) - step7: Divide both sides: \(\frac{4C}{4}=\frac{80}{4}\) - step8: Divide the numbers: \(C=20\) - step9: Substitute the value of \(C:\) \(A=50-20\) - step10: Calculate: \(A=30\) - step11: Calculate: \(\left\{ \begin{array}{l}A=30\\C=20\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}A=30\\C=20\end{array}\right.\) - step13: Rewrite: \(\left(A,C\right) = \left(30,20\right)\) The solution to the system of equations is \( A = 30 \) and \( C = 20 \). This means that 30 adult tickets and 20 child tickets were sold. Therefore, the correct answer is: A) 20 child tickets were sold.

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The Deep Dive

To solve this problem, let's set up a system of equations based on the information given. Let \( x \) be the number of adult tickets and \( y \) be the number of child tickets. From the problem, we have two equations: 1. \( x + y = 50 \) 2. \( 10x + 6y = 420 \) Now, substituting \( x = 50 - y \) into the second equation will help us find the number of child tickets sold! For a practical example, think about this scenario at a real movie theater. You might notice that these sorts of problems reflect actual ticket sales suffered during the pandemic! Analyzing ticket sales helps theaters strategize better pricing to boost attendance when people become more comfortable attending public events again.

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