Problem with cross multiplication

[Trinley]

Hello, I have been poring over this problem for days, and I would really appreciate some help. I'm not sure if it's an algebra problem exactly. It's from my physiology class. The professor said it's simple cross multiplication, and I asked him to explain it again, but I didn't understand his explanation. Here's the problem:

The oxygen carrying capacity of hemoglobin is about 1.34 mL of O2 per gram of hemoglobin (Hb).
Imagine a person with 30 mL O2 per 100 mL of blood.
What would his Hb concentration be?

So I have these two figures:

1.34 mL O2 / 1 g Hb
and
30 mL O2/100 mL blood.

I know the answer is about 22.4 g Hb / 100 mL blood. I know 30/1.34 = 22.4, but I would like to really understand how the problem is set up so that it makes sense to me.

Can anyone help? Thank you.

 

[Prove It]

Hello, I have been poring over this problem for days, and I would really appreciate some help. I'm not sure if it's an algebra problem exactly. It's from my physiology class. The professor said it's simple cross multiplication, and I asked him to explain it again, but I didn't understand his explanation. Here's the problem:

The oxygen carrying capacity of hemoglobin is about 1.34 mL of O2 per gram of hemoglobin (Hb).
Imagine a person with 30 mL O2 per 100 mL of blood.
What would his Hb concentration be?

So I have these two figures:

1.34 mL O2 / 1 g Hb
and
30 mL O2/100 mL blood.

I know the answer is about 22.4 g Hb / 100 mL blood. I know 30/1.34 = 22.4, but I would like to really understand how the problem is set up so that it makes sense to me.

Can anyone help? Thank you.

Set up ratios..

$\displaystyle \begin{align*} O_2 &: \textrm{ Hb } \\ 1.34 &: 1 \\ 1 &: \frac{1}{1.34} \\ 1 &: \frac{100}{134} \\ 1 &: \frac{50}{67} \\ \\ O_2 &: \textrm{ Blood } \\ 30 &: 100 \\ 1 &: \frac{100}{30} \\ 1 &: \frac{10}{3} \\ \\ \textrm{Hb } &: \textrm{ Blood } \\ \frac{50}{67} &: \frac{10}{3} \\ \frac{3}{10} \cdot \frac{50}{67} &: 1 \\ \frac{15}{67} &: 1 \end{align*}$

So the concentration is $\displaystyle \begin{align*} \frac{15}{67} \end{align*}$ mL of Hb to every mL of blood.

 

[Trinley]

That does give the right answer. The professor showed this question in class and asked us calculate it without explaining how. Some people pulled out their phones and gave the answer about 20 seconds. I don't see how they were able to do that. It seems like this way of setting up ratios would take longer and would not be something you can plug into the calculator for a quick answer. Clearly they knew to divide 30 by 1.34, but I don't know how.

The professor showed me that I would just have to set up a simple cross multiplication, but he spoke very quickly and I couldn't follow. Is there a way to set this up as cross multiplication with a minimum of steps?