Answer: 220
Step-by-step explanation:
Children (x): $2
Teens (y): $3, [tex]\frac{3}{4}x[/tex]
Adults: (z): $5
Quantity: x + y + z = 570 ⇒ x + [tex]\frac{3}{4}x[/tex] + z = 570 ⇒ 1.75x + z = 570
Cost: 2x + 3y + 5z = 1950 ⇒ 2x + 3[tex](\frac{3}{4}x)[/tex] + 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): [tex]\frac{3}{4}x[/tex]
y = [tex]\frac{3}{4}(200)[/tex]
= [tex]\frac{600}{4}[/tex]
= 150
Quantity: x + y + z = 570
200 + 150 + z = 570
350 + z = 570
z = 220
