Miss Rojas has a container of Jolly Ranchers on her desk. The ratio of Red Jolly Ranchers to Green Jolly Ranchers is 3 to 7. If there are 42 green jolly ranchers in the container, what is the total amount of Jolly Ranchers in the container?

The total amount of Jolly Ranchers in the container is 60 Jolly Ranchers

Step-by-step explanation:

We have a ratio of

Red Jolly Ranchers : Green Jolly Ranchers

3:7

Sum of the proportion = 3 + 7 = 10

Hence:

Let the total number of jolly ranchers = x

7/10 of x = 42 Green Jolly Ranchers

Hence:

7/10 × x = 42

7x /10 = 42

Cross Multiply

7x = 420

x = 420/7

x = 60 Jolly Ranchers

The total amount of Jolly Ranchers in the container is 60 Jolly Ranchers

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.