Kevin has total of 7590 as currency notes in the denominations of 750, 320 and 10. The ratio of the number of 50 notes and 720 notes is 3:5. If he has a total of 25 notes, how many notes of each denomination are there with him?​

The number of 50 notes = 6

The number of 20 notes = 10

The number of 10 notes = 9

Step-by-step explanation:

The given parameters are;

The total amount Kevin has as currency = 590

The denominations of the notes Kevin has = 50, 20, and 10

The ration of the 50 notes and the 20 notes = 3:5

The total number of notes he has = 25

Therefore, we have;

Let 'x', 'y', and 'z' represent the numbers of 50, 20, and 10 notes Kevin has respectively, we are given the following;

x/y = 3/5...(1)

x + y + z = 25...(2)

50·x + 20·y + 10·z = 590...(3)

Therefore, from equation (1) we get;

x = 3·y/5

By substituting the value of x = 3·y/5 in equations (2) and (3), we get;

For equation (2), we get

x + y + z = 3·y/5 + y + z = 8·y/5 + z = 25

z = 25 - 8·y/5

For equation (3), we get;

50·x + 20·y + 10·z = 50·(3·y/5) + 20·y + 10·z = 50·y + 10·z = 590

∴ z = (590 - 50·y)/10 = 59 - 5·y

Equating the two values of 'z' gives;

25 - 8·y/5 = 59 - 5·y

5·y - 8·y/5 = 59 - 25 = 34

17·y/5 = 34

y = 34/17 × 5 = 10

y = 10

x = 3·y/5 = 3 × 10/5 = 6

x = 6

z = 59 - 5·y = 59 - 5 × 10 = 9

z = 9

Therefore, Kevin has 6, 50 notes, 10, 20 notes and 9, 10 notes

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.

just sum

10 + 10 = 20