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 $159 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 2c+a=67 2 c plus A 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 c+a+s=67
Answers
Answered by
GPT-4o mini
To represent the ticket purchases and their costs through equations, we can break down the information provided for each group:
1. For the **first group**, which purchases 2 child tickets and 1 adult ticket for $67:
- This can be represented as the equation: \(2c + 1a + 0s = 67\) (or simplified to \(2c + a = 67\)).
2. For the **second group**, which purchases 3 child tickets, 1 adult ticket, and 1 senior ticket for $159:
- This can be represented as the equation: \(3c + 1a + 1s = 159\).
3. For the **third group**, which purchases 1 child ticket, 2 adult tickets, and 2 senior tickets for $172:
- This can be represented as the equation: \(1c + 2a + 2s = 172\) (or simplified to \(c + 2a + 2s = 172\)).
Now, looking for similar equations from the options provided:
- \(2c + a = 67\) (correct for the first group's purchase).
- \(3c + a + s = 159\) (correct for the second group's purchase).
- \(c + 2a + 2s = 172\) (correct for the third group's purchase).
Thus, the three equations that could be used to represent the situation are:
1. \(2c + a = 67\)
2. \(3c + a + s = 159\)
3. \(c + 2a + 2s = 172\)
If listed as possible responses:
- \(c + 2a + 2s = 172\)
- \(2c + a = 67\)
- \(3c + a + s = 169\) (this one is incorrect; the correct should be \(3c + a + s = 159\)).
So the correct selections are:
1. \(c + 2a + 2s = 172\)
2. \(2c + a = 67\)
3. \(3c + a + s = 159\) (correct version).
1. For the **first group**, which purchases 2 child tickets and 1 adult ticket for $67:
- This can be represented as the equation: \(2c + 1a + 0s = 67\) (or simplified to \(2c + a = 67\)).
2. For the **second group**, which purchases 3 child tickets, 1 adult ticket, and 1 senior ticket for $159:
- This can be represented as the equation: \(3c + 1a + 1s = 159\).
3. For the **third group**, which purchases 1 child ticket, 2 adult tickets, and 2 senior tickets for $172:
- This can be represented as the equation: \(1c + 2a + 2s = 172\) (or simplified to \(c + 2a + 2s = 172\)).
Now, looking for similar equations from the options provided:
- \(2c + a = 67\) (correct for the first group's purchase).
- \(3c + a + s = 159\) (correct for the second group's purchase).
- \(c + 2a + 2s = 172\) (correct for the third group's purchase).
Thus, the three equations that could be used to represent the situation are:
1. \(2c + a = 67\)
2. \(3c + a + s = 159\)
3. \(c + 2a + 2s = 172\)
If listed as possible responses:
- \(c + 2a + 2s = 172\)
- \(2c + a = 67\)
- \(3c + a + s = 169\) (this one is incorrect; the correct should be \(3c + a + s = 159\)).
So the correct selections are:
1. \(c + 2a + 2s = 172\)
2. \(2c + a = 67\)
3. \(3c + a + s = 159\) (correct version).
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