Can the respiratory quotient be calculated from a formula or must it be measured directly?

I found the following question on the Respiratory quotient:

A normal human diet has a Respiratory quotient (RQ) of approximately 0.85. Given that pure oxidation of fatty acids has a Respiratory quotient (RQ) of 0.7 and pure oxidation of carbohydrates has Respiratory quotient (RQ) of 1, can one determine the fraction between the amount of oxygen used for aerobic respiration of the fat and the amount used for aerobic respiration of the carbohydrates?

My solution:

$$\text{glucose} + \ce{O_2} + \text{fat} + x \, \ce{O_2 \rightarrow} \ce{CO_2} + 0.7x \, \ce{CO_2} \, + \ce{H2O}$$

Note that I haven't balanced the equation excepted for $\ce{O_2}$ and $\ce{CO_2}$ where I added coefficients based on the given RQ. This equation gives $$\text{RC}_{total}=\frac{1+0.7x}{1+x} = 0.85$$

Hence $1+0.7x=0.85(1+x)$, which gives $x=1$, so the amount of oxygen used for Aerobic respiration of the fat and the amount used for Aerobic respiration of the carbohydrates is equal.

Is this correct?

• Note: This is not really homework, but a question that can be seen as a more challenging problem. There are unfortunately no solutions for the challenge problems. Jun 13 '16 at 18:29
• I'm not sure I follow the point of your question? are you just trying to be able to calculate a theoretical RQ based on the theoretical values for oxidizing 100% fat versus 100% glucose? - - - if that is the case, I don't think that's possible - (also, you have ketogenic and glycogenic amino acids that also can be oxidized that will also alter the RQ) Jun 13 '16 at 19:15