a group of 16 people brought tickets to a museum . they paid a total of $56 each adult ticket costs $4 and each child ticket costs $2 formulate and solve a system of equations to determine how many adult tickets and child tickets did they
Let's assume that there were x adult tickets and y child tickets sold.
According to the given information, a group of 16 people bought tickets for a total of $56. Therefore, we can write the first equation as:
4x + 2y = 56
Additionally, the total number of people in the group is 16, so we can write the second equation as:
x + y = 16
Now we have a system of equations:
4x + 2y = 56
x + y = 16
We can solve this system by substitution or elimination. Let's use the method of substitution.
First, solve the second equation for x:
x = 16 - y
Substitute this value of x into the first equation:
4(16 - y) + 2y = 56
64 - 4y + 2y = 56
64 - 56 = 4y - 2y
8 = 2y
4 = y
Substitute the value of y = 4 into the second equation to find x:
x + 4 = 16
x = 16 - 4
x = 12
Therefore, there were 12 adult tickets and 4 child tickets sold.