Question

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

Answer 1

Let c = number of childrenLet t = number of teenagersLet a = number of adults t = 3/4 c 1) c + 3/4 c + a = 5702) 2c + 3 (3/4c) + 5a = 1950 1) 7/4c + a = 5702) 2c + 9/4c + 5a = 1950 1) 7/4c + a = 5702) 17/4c + 5a = 1950 Multiply equation 1 by -51) -35/4c - 5a = -28502)  17/4c + 5a = 1950 Add the equations-18/4c = -900 c = -900 * -4/18 = 200 t = 3/4 c = 150 teenagers

Answer 2

The number of teenagers who attended the concert are:

150

Explanation:

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.

`y=(3)/(4)x`

i.e.

`x=(4)/(3)y--------(3)`

Now, from equation (1) we have:

`z=570-(x+y)`

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

`z=570-((4)/(3)y+y)\\\\i.e.\\\\z=570-(7)/(3)y`

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

`2* (4)/(3)y+3y+5* (570-(7)/(3)y)+2850=1950\\\\i.e.\\\\(8)/(3)y+3y-(35)/(3)y+=1950\\\\i.e.\\\\(8y+3y* 3-35y)/(3)+2850=1950\\\\i.e.\\\\(-18y)/(3)+2850=1950\\\\i.e.\\\\-6y+2850=1950\\\\i.e.\\\\6y=2850-1950\\\\i.e.\\\\6y=900\\\\i.e.\\\\y=150`

Hence, number of children who attended concert= 150