Could someone please help me with this word problem?

The City Zoo has different admission prices for adults and children. When three adults and two children went to the zoo, the bill was $80.88. If two adults and three children got in for $76.47, then what is the price of an adult's ticket and what is the price of a child's ticket?

Thanks

adult ticket --- $x

child ticke ---- $y

3x + 2y = 80.88
2x + 3y = 76.47

1st times 3 ---> 9x + 6y = 242.64
2nd times 2 --> 4x + 6y = 152.94

subtract them:
5x = 89.7
x = 17.94

in 1st
3(17.94) + 2y = 80.88
2y = 27.06
y = 13.53

adult ticket is $17.94
child's ticket is 13.53

To solve this word problem, we can use a system of equations. Let's assign variables to the unknown prices. Let "A" represent the price of an adult ticket, and "C" represent the price of a child ticket.

Based on the information given, we can create two equations.

Equation 1: 3A + 2C = 80.88
Equation 2: 2A + 3C = 76.47

To solve this system of equations, we can use the method of substitution or elimination.

Method 1: Substitution
Solve Equation 1 for A:
3A + 2C = 80.88
3A = 80.88 - 2C
A = (80.88 - 2C) / 3

Substitute this expression for A into Equation 2:
2((80.88 - 2C) / 3) + 3C = 76.47

Simplify and solve for C:
(161.76 - 4C) / 3 + 3C = 76.47
161.76 - 4C + 9C = 229.41
5C = 67.65
C = 67.65 / 5
C ≈ 13.53

Substitute this value back into Equation 1 to find A:
3A + 2(13.53) = 80.88
3A + 27.06 = 80.88
3A = 53.82
A = 53.82 / 3
A ≈ 17.94

So, the price of an adult's ticket is approximately $17.94, and the price of a child's ticket is approximately $13.53.

To solve this word problem, we can set up a system of equations. Let's define the following variables:

- Let the price of an adult's ticket be x
- Let the price of a child's ticket be y

Based on the given information, we can write two equations:

Equation 1: 3x + 2y = 80.88
Equation 2: 2x + 3y = 76.47

We can now solve the system of equations to find the values of x and y.

Using the method of substitution, we can solve for x in Equation 2 and substitute it into Equation 1.

Step 1: Solve Equation 2 for x:
2x + 3y = 76.47
2x = 76.47 - 3y
x = (76.47 - 3y) / 2

Step 2: Substitute x into Equation 1:
3x + 2y = 80.88
3((76.47 - 3y) / 2) + 2y = 80.88
(229.41 - 9y) / 2 + 2y = 80.88
229.41 - 9y + 4y = 161.76
-5y = -67.65
y = -67.65 / -5
y = 13.53

Step 3: Substitute y = 13.53 back into Equation 2 to solve for x:
2x + 3y = 76.47
2x + 3(13.53) = 76.47
2x + 40.59 = 76.47
2x = 76.47 - 40.59
2x = 35.88
x = 35.88 / 2
x = 17.94

Therefore, the price of an adult's ticket is $17.94 and the price of a child's ticket is $13.53.