boomtangboy wrote:
Food -- Number of Calories per Kilogram -- Number of Grams of Protein per Kilogram
S ----- 2.000 -----------------------------------------150
T ----- 1,500 -----------------------------------------90
The table above gives the number of calories and grams of protein per kilogram of foods S and T. If a total of 7 kilograms of S and T are combined to make a certain food mixture, how many kilograms of food S are in the mixture?
(1) The mixture has a total of 12,000 calories.
(2) The mixture has a total of 810 grams of protein.
Responding to a pm:
S -> 2000 C/kg and 150 P/kg
T -> 1500 C/kg and 90 P/kg
The mixture of the two is 7 kg.
Statement 1:
Mixture has 12000 C i.e. 12000/7 C/kg
The average calorie content of the mixture is 12000/7.
wT/wS = (AS - Aavg)/(Aavg - AT) (this formula represents the scale. You can either use the number line or this formula)
wT/wS = (2000 - 12000/7)/(12000/7 - 1500) = 2000/1500 = 4/3
So, in 7 kg, T was 4 kg and S was 3 kg
You don't really need to solve it. From the data you see that you have calorie content of each food and the average calorie content, so you can easily find the ratio of each food in the mixture. You also have the amount of mixture so you can easily find the amount of each food in the mixture.
Statement 2:
Mixture has 810 gms of P i.e. 810/7 P/kg
wT/wS = (150 - 810/7)/(810/7 - 90)
Again, same process as above.
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