Tickets for a concert costs $2 each for children and $5 each for adults. A group of thirty people consisting of children and adults paid a total of $87 for the concert. How many adults were in the group?
number of kids ---- x
number of adults --- 30-x
2x + 5(30-x) = 87
solve for x and the mystery is solved.
To solve this problem, we can set up a system of equations using the given information and then solve it to find the number of adults in the group.
Let's assume the number of children in the group is 'c' and the number of adults is 'a'.
According to the given information, the total number of people in the group is 30, so we can write the equation:
c + a = 30 ---(Equation 1)
The total amount paid for the concert is $87, which can be expressed using the individual ticket prices and the number of children and adults:
2c + 5a = 87 ---(Equation 2)
We now have a system of two equations (Equation 1 and Equation 2) with two variables (c and a). To find the number of adults in the group, we need to solve this system of equations.
One way to solve this system is by using the method of substitution. We can solve Equation 1 for c and substitute it into Equation 2:
c = 30 - a
Substituting this value into Equation 2:
2(30 - a) + 5a = 87
Now we can simplify and solve for a:
60 - 2a + 5a = 87
3a = 27
a = 9
Therefore, there were 9 adults in the group.