Respuesta :
complete question:
5. At a recent Bach concert, total ticket sales were $1,629 Adult tickets cost $9.00 and youth tickets cost $6.00. The number of adult tickets sold was sixteen more than three times the number of youth tickets. How many of each were sold?
Answer:
5.
number of adult ticket sold = 151
number of youth ticket sold = 45
6.
area of the garden = 60ft²
perimeter of the garden = 40 ft
length of hypotenuse = 17 ft
length of the other leg = 15 ft
Step-by-step explanation:
5 .
Total ticket sold = $1,629
let
number of adult ticket sold = a
number of youth ticket sold = b
a = 3b + 16
a - 3b = 16..............(i)
Total sales
9a + 6b = 1629........(ii)
Combine the equations
a - 3b = 16..............(i)
9a + 6b = 1629........(ii)
make a subject of the formula in equation(i)
a = 16 + 3b
Insert the value of a in equation (ii)
9(16 + 3b) + 6b = 1629
144 + 27b + 6b = 1629
33b = 1629 - 144
33b = 1485
b = 1485/33
b = 45
Insert the value of b in equation (i)
a - 3b = 16..............(i)
a - 3(45) = 16
a - 135 = 16
a = 16 + 135
a = 151
6.
The garden is in the shape of a right angle triangle. one leg is 8 ft.
let
a = 8 ft
b = x ft
c = (x + 2) ft
Using Pythagoras theorem
a² + b² = c²
8² + x² = (x + 2)²
64 + x² = (x + 2)(x + 2)
64 + x² = x² + 2x + 2x + 4
64 + x² = x² + 4x + 4
64 = 4x + 4
60 = 4x
x = 60/4
x = 15
Therefore,
a = 8 ft
b = 15 ft
c = 17 ft
Perimeter of the triangle = 8 ft + 15 ft + 17 ft = 40 ft
Area of the triangle = 1/2 × base × height
Area of the triangle = 1/2 × 8 × 15
Area of the triangle = 1/2 × 120
Area of the triangle = 120/2
Area of the triangle = 60 ft²
