Can you please assist with this question:
At a school production, adult tickets cost $7.00 each and student tickets costs $4. The Johnson family is going to the 7:30PM show and will purchase half as many adult tickets as student tickets. If the Johnsons will spend $45 on tickets, how many total tickets did they buy?
X = 7.00 adult ticket
Y = 4.00 student ticket
x + y = 45
1/2x + y = 45 ?
2y+x=$15
15*3=45
number of adult tickets --- x
number of student tickets -- 2x
7x + 4(2x) = 45
15x = 45
x = 3
so they bought 3 adult tickets and 6 student tickets.
check: is the number of adult tickets half of the student tickets ? YES
what is the cost:
7(3) + 4(6) = 45
my answer is correct
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To solve this problem, we need to set up a system of equations to represent the given information.
Let's define the variables:
X = Number of adult tickets
Y = Number of student tickets
We can create the equations based on the given information:
1) The cost equation: The Johnson family spent $45 on tickets.
The cost of each adult ticket is $7, and the cost of each student ticket is $4. So, we can create the equation:
7X + 4Y = 45
2) The ratio equation: The Johnson family purchased half as many adult tickets as student tickets.
The number of adult tickets purchased is half the number of student tickets, so we can create the equation:
X = 0.5Y
Now we have a system of equations:
7X + 4Y = 45 (Equation 1)
X = 0.5Y (Equation 2)
To solve this system, we can use substitution or elimination method.
Let's solve it using the substitution method:
Substitute the value of X from Equation 2 into Equation 1:
7(0.5Y) + 4Y = 45
3.5Y + 4Y = 45
7.5Y = 45
Y = 45 / 7.5
Y = 6
Now we can find the value of X by substituting the value of Y into Equation 2:
X = 0.5(6)
X = 3
Therefore, the Johnson family bought 3 adult tickets and 6 student tickets. In total, they bought 3 + 6 = 9 tickets.