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

2c+a=67
2
𝑐
+
𝑎
=
67
2 c plus A is equal to 67

c+2a+2s=172
𝑐
+
2
𝑎
+
2
𝑠
=
172
c plus 2 A plus 2 s is equal to 172

6c+4a+3s=398
6
𝑐
+
4
𝑎
+
3
𝑠
=
398
6 c plus 4 A plus 3 s is equal to 398

3c+a+s=169
3
𝑐
+
𝑎
+
𝑠
=
169
3 c plus A plus s is equal to 169

c+a+s=67

Answer 1

To represent the situation with equations based on the ticket purchases, we need to analyze the information given for each group.

1. **First Group**: Purchases 2 child tickets and 1 adult ticket for $67.
- This can be represented as: \( 2c + 1a = 67 \)

2. **Second Group**: Purchases 3 child tickets, 1 adult ticket, and 1 senior ticket for $169.
- This can be represented as: \( 3c + 1a + 1s = 169 \)

3. **Third Group**: Purchases 1 child ticket, 2 adult tickets, and 2 senior tickets for $172.
- This can be represented as: \( 1c + 2a + 2s = 172 \)

Now we can summarize the correct equations:

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

**Final Selected Equations**:
- \( 2c + a = 67 \)
- \( 3c + a + s = 169 \)
- \( c + 2a + 2s = 172 \)

Thus, the correct three equations that could be used to represent the situation are:

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