Answer: 300 adults and 450 children
Explanation:
Let the number of adults be x and the number of students be y , then
x + y = 750 ........................... equation 1
the cost of a ticket for adult is $2.50 , that means for x adults , the cost is $2.50x . Also , the cost of ticket for student is $1 , this means that the cost of ticket for y students is $y , writing this in equation form , we have
2.5x + y = 1200 ............................ equation 2
Therefore : the system of linear equations that can be used to find how many adults and how many students attended the concert is
x + y = 750
2.5x + y = 1200
solving the system of linear equation by substitution method , from equation 1 make x the subject of the formula , that is
x = 750 - y ....................... equation 3
substitute x = 750 - y into equation 2 , that is
2.5 ( 750 - y ) + y = 1200
1875 - 2.5y + y = 1200
1875 - 1.5y = 1200
1.5y = 1875 - 1200
1.5y = 675
y = 675/1.5
y = 450
substitute y = 450 into equation 3 , we have
x = 750 - y
x = 750 - 450
x = 300
Therefore , 300 adults and 450 children entered
Explanation: