How do I calculate the ratio to use when combining two products

Question

Hello,

I would be grateful to anyone who can assist. I am trying to calculate the amount of food to use from two different products to feed our dog. The first product, let's call it beef, is made up of 31% protein for each 3/4 of a cup. The second product, let's call it base, is made up of 10.5% protein. If our dog eats 3/4 of a cup of food each day how much beef and how much base would I use to come up with a mixture that is 15% protein?

I thank you and my dog thanks you, in advance.

Greg

Answer 1

Let X = amount of beef

Let Y = amount of base

X + Y = .75

.31X + .105Y = .15(.75) = .1125

I will use substitution rewriting the first equation Y = .75 - X

.31X + .105(.75 - X) = .1125

.31X + .07875 - .105X = .1125

.205X = .03375

X = .165 rounded

Y = .585 rounded

Use about .164 cups of beef and .585 cups of base.