Marianne has a scarf that is 5 inches longer than it is wide. if the area of her scarf is 84 square inches. what are the dimensions of her scarf?

The dimensions of Marianne scarf = 12  × 7  inches

The length of the scarf  =12inches

The width of the scarf = 7 inches

Step-by-step explanation:

Step(i):-

Let 'x' be the width of the scarf

Given that the length of the scarf = x+5

The area of the rectangle = length × width

Given that the area of the rectangle (scarf) = 84 square inches

Step(ii):-

   length × width = 84

    (x+5) × x = 84

    x² + 5x - 84 =0

   x² + 12 x - 7 x - 84 =0

   x(x+12) -7( x+12) =0

    (x-7)(x+12) =0

    x -7 =0  and x+12=0

     x =7   and x= -12

Step(iii):-

We have to choose x =7

The length of the scarf = x+5 = 7+5 =12inches

The width of the scarf = x = 7 inches

tickets for the harlem globetrotters

show at michigan state university in

2010 cost $16, $23, or, for vip seats, $40.

total revenue = 16x + 23y + 40z

if 9 times as many $16 tickets were sold

as vip tickets,

x = 9z => x – 9z = 0, if 9 times as many $16 tickets were sold

as vip tickets,

x = 9z => x – 9z = 0, sales of all three kinds of tickets would

total $46,575.

16x + 23y + 40z = 46575, how many of each kind of ticket would

have been sold?

solve for x, y and z

x − 9z = 0

x − y − z = 55

16x + 23y + 40z = 46575

x = 1170

y = 985

z = 130

welcome!

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.