Question

Ambrose is working at the ticket counter at the aquarium. The first group of the day purchases 2 child tickets and 1 adult ticket and spends $67 before tax. The second group of the day purchases 3 child tickets, 1 adult ticket, and 1 senior ticket, spending $169 before tax. The third group of the day purchases 1 child ticket, 2 adult tickets, and 2 senior tickets, spending $172 before tax. Question Let c represent the number of children's tickets, a represent the number of adult tickets, and s represent the number of senior tickets. Select the three equations that could be used to represent the situation (3 points) Responses c+2a+2s=172 c plus 2 A plus 2 s is equal to 172 c+a+s=67 c plus A plus s is equal to 67 3c+a+s=169 3 c plus A plus s is equal to 169 6c+4a+3s=398 6 c plus 4 A plus 3 s is equal to 398 2c+a=67

Answer 1

To represent the situation with equations based on the information provided, we need to analyze the ticket sales for each group:

1. First Group:

   • Purchases 2 child tickets (c), 1 adult ticket (a), and spends $67.
   • This can be represented as: \[ 2c + 1a + 0s = 67 \quad \text{(Equation 1)} \]

2. Second Group:

   • Purchases 3 child tickets, 1 adult ticket, and 1 senior ticket (s) for a total of $169.
   • This can be represented as: \[ 3c + 1a + 1s = 169 \quad \text{(Equation 2)} \]

3. Third Group:

   • Purchases 1 child ticket, 2 adult tickets, and 2 senior tickets for a total of $172.
   • This can be represented as: \[ 1c + 2a + 2s = 172 \quad \text{(Equation 3)} \]

Now, if we summarize the correct equations from the options provided:

1. \( 2c + a = 67 \) (or \(2c + 1a + 0s = 67\))
2. \( 3c + a + s = 169 \)
3. \( c + 2a + 2s = 172 \)

From the list of responses provided, these match:

• \( 2c + a = 67 \)
• \( 3c + a + s = 169 \)
• \( c + 2a + 2s = 172 \)

Therefore, the three equations that represent the situation are:

1. \( 2c + a = 67 \) (First Group)
2. \( 3c + a + s = 169 \) (Second Group)
3. \( c + 2a + 2s = 172 \) (Third Group)