Charlotte and savannah go to the movie theater and purchase refreshments for their friends. charlotte spends a total of $85.00 on 8 bags of popcorn and 10 drinks. savannah spends a total of $20.50 on 2 bags of popcorn and 2 drinks. write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.

The system of equations that can be used to find the price of one bag of popcorn and the price of one drink are:

8p + 10d = 85

2p + 2d = 20.50

Step-by-step explanation:

Let the price of a bag of popcorn be p

Let the price of one drink be d

Charlotte spends a total of $85.00 on 8 bags of popcorn and 10 drinks. This means

8p + 10d = 85

Savannah spends a total of $20.50 on 2 bags of popcorn and 2 drinks.

2p + 2d = 20.50

The system of equations that can be used to find the price of one bag of popcorn and the price of one drink are:

8p + 10d = 85 1

2p + 2d = 20.50 - - - - - -2

Solving the equations with elimination method, multiply equation 1 by 2 and equation 2 by 8

16p + 20d = 170

16p + 16d = 164

Subtracting,

4d = 6

d = 6/4 = $1.5

Put d = 2 in equation 1

8p + 15 = 85

p = 70/8 = $8.75

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.