Hi all. Some questions i cant figure out on the above mentioned
topics.
Matrices: I think some of the word problems can be a bit tricky,
as in i dont know how to form the correct matrix. Take for
example:
A food manufacturer invents a new flavour of meatball from
several ingredients. The main ingredients are beef, chicken and
fish.
100g of beef contributes 20g of proteins, 30g of fats and 0.5g
of cholesterol. 100g of chicken contributes 45g of proteins, 30g of
fats and 0.2g of cholesterol. 100g of fish contributes 75g of
proteins, 20g of fats and 0.2g of cholesterol. The key nutritional
requirements for each 100g of mixture of meatball are 60g of
proteins, 20g of fats and 0.2g of cholesterol. Other ingredients do
not contribute to these three key nutritional requirements.
Find the amount of beef, chicken and fish the food manufacturer
should include in 1 kg of mixture to meet the nutritional
requirements.
First of all, i let the amount of beef, chicken and fish be x,y,
and z respectively. Then after that i’m stuck.
Thanks, really appreciated.
Hi,
Since we have 3 unknowns to be found, we will need to
form 3 equations. Also, one needs to be clear about the measurement
unit of x, y and z. In this case, we use gram as the unit.
Now read the question carefully to see possible
relationships which may be formed.
We need 1 kg (1000 g) of mixture. For this amount of
mixture, how much proteins, fats and cholestrol will there be?
For proteins in 1000g of mixture, how much is contributed
by each of x, y and z? That will give us an equation.
For fats and cholestrol in 1000g of mixture, ask the same
question. That should give us another 2 equations.
This process of question analysis can be applied to other
questions of a similar nature.
Thanks!
Cheers,
Wen Shih
