Danny brought $23.75 to the state fair. He bought a burger, a souvenir, and a pass. The burger was 1/4 as much as the souvenir, and the souvenir cost 2/3 the cost of the pass. Danny had $4.50 left over after buying these items. What was the cost of each item?

cost of pass = $10.5

cost of souvenir = $7

cost of burger = $1.75

Step-by-step explanation:

Total money with Danny = $23.75

Let the cost of pass be $x

As the  souvenir cost 2/3 the cost of the pass

Thus cost of souvenir = $(2/3)x

Cost of burger is 1/4 of souvenir

Thus cost of burger = (1/4)*(2/3)x =$ 1/6x

Total cost of all the three item in terms of x

x + (2/3)x + ( 1/6)x

=>(6x+4x+x)/6 = 11x/6

Given that after money spent on buying all the three thing he has left $4.50

subtracting money spent on buying three things from total money is equal to $4.50

Mathematically it can be written as

$23.75 -  11x/6 = $4.50

=> $23.75  - $4.50=  11x/6

=>$19.25 =  11x/6

=> $19.25*6 = 11 x

=> $115.5 = 11x

=> $115.5/11 = x

=> x = 10.5

Thus,

cost of pass = x = $10.5

cost of souvenir = $(2/3)x =$(2/3)*10.5 = $7

cost of burger = $ 1/6x = $ (1/6)*10.5 = $1.75

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80