The Science Museum charges $14 for adult admission and $11 for each child. The total bill for 68 people from a school field trip was $784. How many adults and how many children went to the museum?
A = number of adults
C = number of childs
Adults + Childs= 68 people
Field trip was $784
A • $14 + C • $11 = $784
Now solve system:
A + C = 68
14 A + 11 C = 784
Solution is:
A = 12 , C = 56
12 adults and 56 childs
To solve this problem, we can set up a system of equations. Let's assume 'a' represents the number of adults and 'c' represents the number of children attending the Science Museum.
According to the given information, the price of adult admission is $14 and the price for each child is $11. The total bill for 68 people was $784.
Using the equation for the total bill, we have:
14a + 11c = 784
We also know that the total number of people in the field trip was 68. Therefore, we can create an equation for the total number of people:
a + c = 68
Now, we can solve the system of equations to find the values of 'a' and 'c'.
One way to solve this system is by using substitution. We can solve the second equation for 'a' and substitute it into the first equation.
From the second equation, we have:
a = 68 - c
Substituting this value of 'a' into the first equation, we can solve for 'c':
14(68 - c) + 11c = 784
952 - 14c + 11c = 784
-3c = 784 - 952
-3c = -168
Dividing both sides of the equation by -3, we get:
c = -168 / -3
c = 56
Now that we have the value of 'c' (the number of children), we can substitute it back into the second equation to solve for 'a':
a + 56 = 68
a = 68 - 56
a = 12
Therefore, there were 12 adults and 56 children who went to the museum.
Let's assume the number of adults is x, and the number of children is y.
According to the given information, the Science Museum charges $14 for each adult admission and $11 for each child admission.
The total bill for 68 people from the school field trip was $784.
We can set up the following system of equations:
x + y = 68 (equation 1)
14x + 11y = 784 (equation 2)
To solve this system of equations, we can use either substitution or elimination method.
Let's use the substitution method.
From equation 1, we can isolate x, so we have:
x = 68 - y
Substitute the value of x from equation 1 into equation 2:
14(68 - y) + 11y = 784
Simplify the equation:
952 - 14y + 11y = 784
952 - 3y = 784
-3y = 784 - 952
-3y = -168
y = -168 / -3
y = 56
Substitute the value of y into equation 1 to find x:
x + 56 = 68
x = 68 - 56
x = 12
So, there were 12 adults and 56 children who went to the Science Museum.