You are making balloon arrangements for a birthday party. there are 16 white balloons and 24 red balloons . each arrangement must be identical .what is the greatest number of arrangements you can make using every balloon

The greatest number of arrangements using every balloon is an illustration of the highest common factors (HCF).

The greatest number of arrangements you can make using every balloon is 8.

Given that:

To determine the greatest number of arrangements, we simply calculate the HCF of 16 and 24.

We have:

The highest common factor is:

Hence, the greatest number of arrangements you can make using every balloon is 8.

Read more about highest common factors (HCF) at:

link

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

figure c

step-by-step explanation:

hope this .