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

Question

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

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Madelyn 4 weeks 2021-09-16T02:47:46+00:00 1 Answer 0

Answers ( )

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    2021-09-16T02:49:19+00:00

    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

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