... Assuming that the locust eats exactly
100 mg of food per day, determine how many milligrams of food X and food Y the locust
needs to eat per day to reach the desired intake balance between protein and carbohydrate
HELP ME?
- Posted:
- 3+ months ago by Lady Midn...
- Topics:
- locust
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Added 3+ months ago:
Scientific studies suggest that some animals regulate their intake of different types of food available in the environment to achieve a balance between the proportion, and ultimately the total amount, of macro-nutrients consumed. Macro-nutrients are categorized as protein, carbohydrate or fat/lipid. A seminal study on the macro-nutrient intake of migratory locust nymphs (Locusts migratory) suggested that the locust nymphs studied sought and ate combinations of food that balanced the intake of protein to carbohydrate in a ratio of 45:55 [1].
Assume that a locust nymph finds itself in an environment where only two sources of food are available identified as food X and food Y . Food X is 27% protein and 73% carbohydrate, whereas food Y is 73% protein and 27% carbohydrate. Assuming that the locust eats exactly 100 mg of food per day, determine how many milligrams of food X and food Y the locust needs to eat per day to reach the desired intake balance between protein and carbohydrate.
Answers (2)
Get a ruler in your hands. Measure things until you start to understand how a ruler works. Measure some stuff and figure out where the center is. Say you measure a book and it's 7/8" thick. You look at your ruler and see that every eighth is divided into two sixteenths, so obviously half of 7/8" is going to be 7/16". If you write that out you have 1/2 x 7/8 = 7/16. And you notice that 1/2 is divided into 2/4 and then into 4/8 and so on, so you can convert anything to anything by multiplying all the numbers on top and then all the numbers on bottom.
Other rulers are divided into 10 and 100 parts. But an inch is still an inch, so anything on one ruler can be translated to the other ruler. A half inch on one ruler is 5/10 or 50/100 on the other. An eighth inch is just 12.5 marks when you have 100 marks per inch. A metric ruler divides an inch into 25.4 parts, so a half inch would be 12.7 of those parts. Pretty simple, isn't it? Practice this a bit and people will think you went to wizard school.
Percent is simply a ruler with 100 marks. The only confusion is trying to keep track of what the marks represent, since that changes from time to time.
The given ratio of 45:55 addds to 100 parts, so we are talking about percent: 45% and 55%. The totals must equal 45 mg protein and 55 mg carbs.
Food X is 27% protein and 73% carb. Food Y is 73% protein and 27% carb. So we build equations now.
0.27X + 0.73Y = 45
0.73X + 0.27Y = 55
X + Y = 100
Rewrite the third equation:
Y = 100 - X
Substitue that into the first equation:
0.27 X + 0.73(0.27X) = 45
0.27X + 0.1971X = 45
There are several ways to solve this, but the easy way is to use a plotter program
www.wolframalpha.com/input/?i=solve+0.27X+%2B+0.73Y+%3D+45,+0.73X+%2B+0.27Y+%3D+55
This is called "simultaneous equations" and it is a bit complicated for discussing bugs. What sort of a class are you taking that requires such intricate math? The only field I know of is nursing, and they teach simpler methods.
Sorry I misses out what is the actually answer?
Bla bla math stories.
Need: Mix Z = 45% protein + 55% carbs.
1mg of X = 27% protein + 73% carbs.
1mg of Y = 73% protein + 27% carbs.
Total intake = 100mg.
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Denote protein := p, carbs := c. Denote quantities eaten in mg as n, m.
n * X + m * Y = 100 * Z
n + m = 100
n * (0.27p + 0.73c) + m * (0.73p + 0.27c) = 100 * (0.45p + 0.55c)
0.27n*p + 0.73n*c + (100 - n) * (0.73p + 0.27c) = 45p + 55c
0.27n*p + 0.73n*c + 73p + 27c - 0.73n*p - 0.27n*c = 45p + 55c
-0.46np + 0.46nc = -28p + 28c
Match each coefficient in the equation.
-0.46n = -28, 0.46n = 28
n = 60.87
m = 39.13
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60.87 * 27% + 39.13 * 73% = 16.43 + 28.56 ~ 45
60.87 * 73% + 39.13 * 27% = 44.44 + 10.57 ~ 55
Generally, I'm not sure the equations necessarily have to match as they did here. The ratio symmetry is likely what gives them that property, anywhere from 27% to 73%. That can be proven by defining the ratios as r1 / r2 / r3 and 100 - r counterparts, but cba.
Jv's explanation is clearer, but there's an error in the substitution part. Need to add 100 - cX.
Withdrawing the last comment, (100 - r1)n + (100 - r2)n = (100 - r3)(n+m) perfectly cancels out the constants, so solving both sides is theoretically unnecessary..
General equation, courtesy of wolfram:
m = t(r1 - r3) / (r1 - r2)
n = t(r3 - r2) / (r1 - r2)
Where t = n + m.
Apologies, I have posted all the information given related to the question.