At a book fair, 1/4 of the people bought 1 book.3/5 of the remaining
people bought 2 books each and the rest of the people bought 3
books each. a total of 4469 books were sold. how many people
were at the book fair?

2,180 people

Step-by-step explanation:

Let

x> number of people at the book fair

we know that

1) 1/4 of the people bought 1 book each

(1/4)x=(5/20)x

2) 3/5 of the remaining  people bought 2 books each

The remaining people is (3/4)x

so

(3/5)(3/4)x=(9/20)x

3) the rest of the people bought 3  books each

The rest of the people is x-(5/20)x-(9/20)x=(6/20)x

The linear equation that represent this situation is

(1)*(5/20)x+(2)*(9/20)x+(3)*(6/20)x=4,469

(5/20)x+(18/20)x+(18/20)x=4,469

(41/20)x=4,469

x=4,469*20/41

x=2,180 people

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.