How Do Isotope Tracers Determine Mixing Ratios in Water Samples?

[geojon]

Homework Statement

Two water samples are mixed. Sample 1 has δ¹⁸O-H₂O = -1(per mil), Sample 2 has δ¹⁸O-H₂O = -20 (per mil), and the mixture has δ¹⁸O-H₂O = -15 (per mil).

What fraction of water came from sample 1 and what fraction came from sample 2?
Assume that F = the fraction of the water that came from Sample 1
Assume that 1-F = the fraction of the water that came from Sample 2

Homework Equations

Q_T=Q₁+Q₂ where Q_T is total percent, and Q1 and Q2 are the percent contributions to the mixture from samples 1 and 2, respectively.

δ¹⁸O_TQ_T = δ¹⁸O₁Q₁+δ¹⁸O₂Q₂

The Attempt at a Solution

I've uploaded my work...if I am using the write mixing equation for two endmembers, my problem really is then just isolating and solving for F. From there I can solve for F₂

 

[geojon]

@Greg Bernhardt I've used the Isotopic Mixing Equation: δ¹⁸O_TQ_T = δ¹⁸O₁Q₁+δ¹⁸O₂Q₂ in order to solve it. It can also be solved using a Two-component Mixing Model, according to the equations: F₂ = (δ¹⁸O_mix-δ¹⁸O₁) / (δ¹⁸O₂-δ¹⁸O₁) ; F₁ = 1 - F₂
Using both equations, you find that the fraction of the sample coming from sample 1 is 0.26 (or 26%), and percent contribution from sample 2 is 0.74 (or 74%)