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. Three-fourths as many teenagers as children attended. How many adults attended?

Answer 1

Answer: 220

Step-by-step explanation:

Children (x): $2

Teens (y): $3, $\frac{3}{4}x$

Adults: (z): $5

Quantity: x + y + z = 570  ⇒  x + $\frac{3}{4}x$ + z = 570  ⇒ 1.75x + z = 570  

Cost: 2x + 3y + 5z = 1950  ⇒  2x + 3$(\frac{3}{4}x)$ + 5z = 1950  ⇒  2x + 2.25x + 5z = 1950  ⇒  4.25x + 5z = 1950

Qty:    1.75x +  z =  570  →  5(1.75x +  z =  570)  →    8.75x + 5z = 2850

Cost: 4.25x + 5z = 1950 → -1(4.25x + 5z = 1950 → -4.25x - 5z = -1950

                                                                                  4.50x        =   900

                                                                                          x       =    200

Teens (y): $\frac{3}{4}x$

           y = $\frac{3}{4}(200)$

             = $\frac{600}{4}$

             = 150

Quantity: x + y + z = 570  

              200 + 150 + z = 570

                     350     + z = 570

                                    z = 220