Cindy is selling tickets. The first day she sold 8 adult tickets and 5 child tickets for a total for $180.50 in sales. The second day she received $261 for 12 adult tickets and 5 child tickets. What is the price of an adult ticket? What is the price of a child ticket?
Write two algebraic expression and solve using the elimination method, substitution method, or graphical method.
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www.algebra.com/algebra/homework/Systems-of-equations/Systems-of-equations.faq.question.1135264.html
To find the price of an adult ticket and the price of a child ticket, we can set up a system of equations using the given information.
Let's denote the price of an adult ticket as 'x' and the price of a child ticket as 'y'.
From the given information, we can create the following equations:
Equation 1: 8x + 5y = 180.50
Equation 2: 12x + 5y = 261
To solve this system of equations, we can use either the elimination method or the substitution method. Let's solve it using the substitution method:
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve Equation 1 for 'y':
8x + 5y = 180.50
5y = 180.50 - 8x
y = (180.50 - 8x) / 5
Step 2: Substitute the expression for 'y' in terms of 'x' into the other equation.
Substitute (180.50 - 8x) / 5 for 'y' in Equation 2:
12x + 5((180.50 - 8x) / 5) = 261
Simplify this equation:
12x + 180.50 - 8x = 261
12x - 8x + 180.50 = 261
4x + 180.50 = 261
Step 3: Solve for 'x':
4x = 261 - 180.50
4x = 80.50
x = 80.50 / 4
x = 20.125
So, the price of an adult ticket is $20.125.
Step 4: Substitute the value of 'x' back into Equation 1 to solve for 'y':
8x + 5y = 180.50
8(20.125) + 5y = 180.50
161 + 5y = 180.50
5y = 180.50 - 161
5y = 19.50
y = 19.50 / 5
y = 3.90
So, the price of a child ticket is $3.90.
Therefore, the price of an adult ticket is $20.125, and the price of a child ticket is $3.90.
$X = cost of an adult ticket.
$Y = cost of a child's ticket.
Eq1: 8x + 5y = 180.50.
Eq2: 12x + 5y = 261.
Subtract Eq2 from Eq1 and solve for X.
-4x = -80.5,
X = 20.125.
In Eq2, replace X with 20.125 and solve for Y.
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