Elise is making punch for the party that requires 2 parts of fruit juice for every 5 parts of ginger ale. To make the punch, she uses 18 ounces of fruit juice and 3 containers of ginger ale. How many ounces are in each container of ginger ale?

Given:

Elise is making punch for the party that requires 2 parts of fruit juice for every 5 parts of ginger ale.

To make the punch, she uses 18 ounces of fruit juice and 3 containers of ginger ale.

To find:

The number of ounces in each container of ginger ale.

Solution:

Let n be the number of ounces in each container of ginger ale.

According to the question, the ratio of fruit juice and ginger ale is 2:5. it means,

Divide both sides by 2.

So, ginger required for punch is 45 ounces.

Number of containers = 3

Number of ounces in each container of ginger ale = n

Number of ounces in 3 containers of ginger ale = 3n

Now,

Divide both sides by 3.

Therefore, 15 ounces are in each container of ginger ale.

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!