So I have a problem with ratios that I need to sort out.
I want to know how much of each of two types of food I need to eat in order to get a fixed amount of protein and carbs.
an example…
I want to eat 33g of protein and 44g or carbs in one meal (more importantly a ratio of 0.75 protein to carbs for this meal).
My two foods are
chicken (28.9g protein, 0.5g carbs per 100g)
pasta (6g protein, 31g carbs per 100g)
So, how many grams of chicken and how many grams of pasta do I eat in order to get 33g protein, 44g carbs?
Thanks
Best Answer
Fun question. We can write the following equations:
28.9x + 6y = 33; 0.5x + 31y = 44
Which gives us x = .85, y = 1.4 (roughly).
So 85 grams of chicken, and 140 grams of pasta.
I see that this is an example, and not the problem you want solved, so let me elaborate further.
Let x be the factor of 100 g of chicken you have to eat. Let y be the factor of 100 g of pasta you have to eat. Since we know how much protein is in 100 grams of both food, the total protein is:
28.9x + 6y = protein
And similarly, the total amount of carbs is
0.5x + 31y = carbs
Now, you know your goal, so set the "protein" equation to 33 and the "carbs" equation to 44.
28.9x + 6y = 33 0.5x + 31y = 44
Now, we can find x and y with some basic algebra. First, solve for x in the first equation. Then, plug that result into the second equation's x. Then, you can find the value of y. This allows you to find the value of x, by plugging y's numeric value into either equation.
When you have x and y, you have the factors of 100g for chicken and pasta, so 100x and 100y are the numbers you seek.