Brown's grounds coffee is selling for $2.50 a pound is mixed with coffee from heaven selling for $2.80 a pound to produce 100 pounds of a blend selling for $2.62 per pound. how many pounds of each kind of coffee were mixed?

the number of pounds of Brown's Grounds Coffee that was mixed is 60

the number of pounds of Coffee From Heaven that was mixed is 40

Step-by-step explanation:

Let x represent the number of pounds of Brown's Grounds Coffee that was mixed.

Let y represent the number of pounds of Coffee From Heaven that was mixed.

Brown's Grounds Coffee is selling for $2.50 a pound is mixed with Coffee From Heaven selling for $2.80. 100 pounds was produced and sold at the rate of $2.62 per pound. This means that the total cost of the blend produced is 100×2.62 = $262. Therefore

2.5x + 2.8y = 262 - - - - - -- - -- - -1

x + y = 100

Substituting x = 100 - y into equation 1, it becomes

2.5(100 - y) + 2.8y = 262

250 - 2.5y + 2.8y = 262

- 2.5y + 2.8y = 262 - 250

0.3y = 12

y = 12/0.3 = 40

x = 100 - y = 100 - 40

x = 60

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.

there still no table