Math experts: I need your help w/ solving math problems for work

[Nikia]

I feel so like such an idiot because I know that I should be able to figure out the solution mathematically. Instead, I guess and plug numbers, wasting my time.
Here is an example of a problem that I am looking to solve:
I am attempting to match a formulation.
The product contains (c)% of a nutrient
There are two ingredients in the product. We know the usual amount of nutrient in these two ingredient.
Ingredient x: (a)% nutrient
Ingredient y: (b)% nutrient
We know that x+y= (z)% of the total formula
a+b=c
We want to know what % is ingredient x and what percent is ingredient is y.

How do I solve this? I remember solving similiar problems in calculus, but that was 10 years ago and I am completely out of practice. No one at work is able or willing to help me.

I apologize for the variables. I hope that it is not too confusing. If you could explain how to solve it for me, I will be extremely greatful.

[Nikia]

1. Self kick

I know that this is kind of a heavy topic for Friday night.
If this doesn't get responses, perhaps I'll PM some people who might have a better handle on this topic than me.

[aePrime]

2. Hopefully I understand you correctly

I'm going to use concrete numbers, because this gets rather messy symbolically.

Let's say that we know x and y make up 75% of a product (p).
Let's also say that 80% of x is made up of the nutrient, and that 90% of y is made up of the nutrient. We know that the product is made up of 63% of the nutrient.

These are all of the knowns, as I understand it:

x + y = .75p
.8x + .9y = .63p

Solve the first equation for x:
x = .75p - y

Substitute that value for x into the second equation:
.8(.75p - y) + .9y = .63p
.6p - .8y + .9y = .63p
.6p + .1y = .63p
.1y = .03p
y = .3p

We now know that y makes up 30% of the product. We can now substitute that into the first equation:
x + .3p = .76p
x = .45p

We now know that x makes up 45% of the product.

[Nikia]

3. Thanks

When I was trying to figure it out at work, I think that I was making it more difficult than that. For some reason, I had overlooked the approach that you gave.