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boomtangboy
Joined: 06 Jan 2012
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Status:May The Force Be With Me (D-DAY 15 May 2012)
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Updated on: 01 Oct 2022, 09:18
Originally posted by boomtangboy on 01 Apr 2012, 05:26.
Last edited by Bunuel on 01 Oct 2022, 09:18, edited 4 times in total.
Last edited by Bunuel on 01 Oct 2022, 09:18, edited 4 times in total.
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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.
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01 Apr 2012, 08:15
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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 --> say x kilograms of food S are in the mixture then there will be 7-x kilograms of food T in the mixture. Now, according to the table above we'll have: 2,000x+1,500(7-x)=12,000, since there is only one variable then we can solve for it. Sufficient.
(2) The mixture has a total of 810 grams of protein --> 150x+90(7-x)=810, since there is only one variable then we can solve for it. Sufficient.
Answer: D.
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 --> say x kilograms of food S are in the mixture then there will be 7-x kilograms of food T in the mixture. Now, according to the table above we'll have: 2,000x+1,500(7-x)=12,000, since there is only one variable then we can solve for it. Sufficient.
(2) The mixture has a total of 810 grams of protein --> 150x+90(7-x)=810, since there is only one variable then we can solve for it. Sufficient.
Answer: D.
General Discussion
25 Jul 2012, 21:34
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boomtangboy
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.
