Question

admission to a carnival is $4 for children and $6 for adults. a group of 21 people pays $900 for admission to the carnival. what is the ratio of the number of children to the number of adults in this group?

Answer 1

To determine the ratio of children to adults in the group, set up and solve a system of equations using the given admission prices and total number of people. The equations are based on the cost per child, cost per adult, and total cost for the group.

Step-by-step explanation:

To find the ratio of the number of children to the number of adults in the group, we can set up a system of equations based on the admission prices and the total number of people. Let's denote the number of children as c and the number of adults as a. According to the question:

• The admission fee for children is $4, and for adults is $6.
• The total number of people is 21, so c + a = 21.
• The total amount paid for admission is $900.
• Therefore, the total cost equation is 4c + 6a = 900.

Solving the system:

1. Multiply the first equation by 4: 4c + 4a = 84.
2. Subtract this equation from the total cost equation: (4c + 6a) - (4c + 4a) = 900 - 84, simplifying to 2a = 816.
3. Divide by 2 to find a = 408.
4. Substitute a back into the first equation to find c.
5. After solving 4c + 6a = 900 by putting a = 408, then c=387.
6. Ratio of c:a = 129 : 136

The solution gives us the number of children and adults, from which we can calculate the ratio.

Answer 2

To find the ratio of children to adults in the group, we set up and solved a system of equations. However, a mistake was made during calculation resulting in an incorrect negative number for the children. It is imperative to go back and re-calculate to correct the errors.

Step-by-step explanation:

To find the ratio of the number of children to the number of adults in a group that paid $900 for admission to a carnival, we need to set up a system of equations based on the given information. Let's denote the number of children as C and the number of adults as A.

We know the following information:

• The admission fee is $4 for children and $6 for adults.
• The group comprises 21 people.
• The total amount paid for admission is $900.

The two equations that represent this situation are:

1. C + A = 21 (total number of people)
2. 4C + 6A = 900 (total cost)

Now we can solve the system of equations. To do this, we can multiply the first equation by 4 to match the coefficient from the second equation for C.

4C + 4A = 84

Subtracting this from the second equation:

6A - 4A = 900 - 84

2A = 816

A = 408 / 2

A = 204

Now, substitute the value of A into the first equation:

C + 204 = 21

C = 21 - 204

C = -183

However, since the number of people cannot be negative, we know that we made a calculation error. We actually need to use the number A = 816 / 2 = 408 and the correct equation is C + A = 21, therefore:

C = 21 - A

C = 21 - 408/2

C = 21 - 204

C = -183

There's clearly another mistake since we still have a negative number of children. We should reconsider the correct values for C and A in our calculations. In such cases, it's important to double-check each mathematical operation for potential errors.