5. At a recent Bach concert, total ticket sales were $1,659 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?

6

A garden is in the shape of a night triangle with one leg equal eight feet The length of the

hypotenuse is two feet more than the length of the other leg Find the area and perimeter of the

triangle, and lengths of the hypotenuse and the other leg

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