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
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+2a+2s=172
𝑐
+
2
𝑎
+
2
𝑠
=
172
c plus 2 A plus 2 s is equal to 172
2c+a=67
2
𝑐
+
𝑎
=
67
2 c plus A is equal to 67
c+a+s=67
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
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+2a+2s=172
𝑐
+
2
𝑎
+
2
𝑠
=
172
c plus 2 A plus 2 s is equal to 172
2c+a=67
2
𝑐
+
𝑎
=
67
2 c plus A is equal to 67
c+a+s=67
Answers
GPT-4o mini
To represent the situation with equations based on the groups purchasing tickets, we need to define the variables correctly and write equations based on the information provided.
We have:
- Let \( c \) be the cost of a child's ticket.
- Let \( a \) be the cost of an adult ticket.
- Let \( s \) be the cost of a senior ticket.
The purchases of each group can be translated into linear equations as follows:
1. **First Group (2 child tickets and 1 adult ticket):**
\[
2c + 1a = 67
\]
This corresponds to the equation \( 2c + a = 67 \).
2. **Second Group (3 child tickets, 1 adult ticket, and 1 senior ticket):**
\[
3c + 1a + 1s = 169
\]
This corresponds to the equation \( 3c + a + s = 169 \).
3. **Third Group (1 child ticket, 2 adult tickets, and 2 senior tickets):**
\[
1c + 2a + 2s = 172
\]
This corresponds to the equation \( c + 2a + 2s = 172 \).
Now, let's summarize the three equations we identified:
1. \( 2c + a = 67 \)
2. \( 3c + a + s = 169 \)
3. \( c + 2a + 2s = 172 \)
Based on the options you've provided, the correct three equations to represent the situation are:
1. \( 2c + a = 67 \) (First Group)
2. \( 3c + a + s = 169 \) (Second Group)
3. \( c + 2a + 2s = 172 \) (Third Group)
Thus, the responses you should select are:
- \( 2c + a = 67 \)
- \( 3c + a + s = 169 \)
- \( c + 2a + 2s = 172 \)
We have:
- Let \( c \) be the cost of a child's ticket.
- Let \( a \) be the cost of an adult ticket.
- Let \( s \) be the cost of a senior ticket.
The purchases of each group can be translated into linear equations as follows:
1. **First Group (2 child tickets and 1 adult ticket):**
\[
2c + 1a = 67
\]
This corresponds to the equation \( 2c + a = 67 \).
2. **Second Group (3 child tickets, 1 adult ticket, and 1 senior ticket):**
\[
3c + 1a + 1s = 169
\]
This corresponds to the equation \( 3c + a + s = 169 \).
3. **Third Group (1 child ticket, 2 adult tickets, and 2 senior tickets):**
\[
1c + 2a + 2s = 172
\]
This corresponds to the equation \( c + 2a + 2s = 172 \).
Now, let's summarize the three equations we identified:
1. \( 2c + a = 67 \)
2. \( 3c + a + s = 169 \)
3. \( c + 2a + 2s = 172 \)
Based on the options you've provided, the correct three equations to represent the situation are:
1. \( 2c + a = 67 \) (First Group)
2. \( 3c + a + s = 169 \) (Second Group)
3. \( c + 2a + 2s = 172 \) (Third Group)
Thus, the responses you should select are:
- \( 2c + a = 67 \)
- \( 3c + a + s = 169 \)
- \( c + 2a + 2s = 172 \)