# There are 3 foods with the following Protein/Fat/Carbs (grams/ounce): 2,3,4; 3,3,1; 3,3,2. We want a meal using the 3 foods that results in 24g of protein, 27g of fat, 20g of carbs. How much of each food is needed?

##### 1 Answer

#### Explanation:

I'm going to use the Food letters - A, B, C - to be the number of ounces of that food that should be used.

I'm going to put the chart here (numbers in grams/ounce):

And we need 24g of Protein, 27g of Fat, 20g Carbs, so:

(P)rotein:

(F)at:

(C)arbs:

I'm first going to work on expressing the B values in terms of A and C. I'll do that by subtracting

3C:

P:

3C:

F:

And I can now subtract

And now we can substitute this back in to one of our equations (I'll do both to double check our answer this far - I'll use colours to help highlight what we're doing):

Ok - C checks out as equaling 2. Now let's substitute into one of the originals (and I'll do all 3 to show it works in all the original equations):

(P)rotein:

(P)rotein:

(P)rotein:

(P)rotein:

(P)rotein:

(F)at:

(F)at:

(F)at:

(F)at:

(F)at:

(C)arbs:

(C)arbs:

(C)arbs:

(C)arbs:

Everything checks out!