Tickets to a concert cost $2 for children, $3 for teenagers, and $5 for adults . when 570 people attended the concert, the total ticket receipts were $1950. compared to the number of children in attendance, three-fourths as many teenagers attended. how may teenagers attended

The number of teenagers who attended the concert are:

                                150

Tickets to a concert cost $2 for children, $3 for teenagers, and $5 for adults.

Let number of children who attended the concert= x

Number of teenager who attended the concert= y

Number of adults who attended the concert= z

When 570 people attended the concert, the total ticket receipts were $1950.

i.e. the equations that are made with the help of above information is:

x+y+z= 570----------(1)

2x+3y+5z= 1950--------(2)

Also,Compared to the number of children in attendance, three-fourths as many teenagers attended.

i.e.

i.e.

Now, from equation (1) we have:

On putting the value of x from equation (3) we have:

on putting the value of z and x in terms of y in equation (2) we have:

Hence, number of children who attended concert= 150

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )

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