Let x and y be the 2 parts of 15 ==> x + y=15 (given)
Reciprocal of x and y ==> 1/x +1/y ==> 1/x + 1/y = 3/10 (given)
Let's solve 1/x + 1/y = 3/10 . Common denominator = 10.x.y (reduce to same denominator)
==> (10y+10x)/10xy = 3xy/10xy ==> 10x+10y =3xy
But x+y = 15 , then 10x+10y =150 ==> 150=3xy and xy = 50
Now we have the sum S of the 2 parts that is S = 15 and their Product = xy =50 Let's use the quadratic equation for S and P==> X² -SX +P =0 Or X² - 15X + 50=0, Solve for X & you will find: The 1st part of 15 is 10 & the 2nd part is 5
For the first sugar and servings part, 4 for sugar, 2 for servings.
The ratio for this example above it for sugars to servings it 2:1. So every 2 sugars is every 1 serving and this applies to every other of the sugars and servings in the table.
