SOLUTION: Gardeners on a low carb diet are interested in knowing the carbohydrate content of the vegetables they plant. Together, 1 cup of raw lettuce, 6 raw asparagus spears, and 1 cup of r

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Question 1199025: Gardeners on a low carb diet are interested in knowing the carbohydrate content of the vegetables they plant. Together, 1 cup of raw lettuce, 6 raw asparagus spears, and 1 cup of raw tomatoes contain 12 grams of carbohydrates. One cup of raw lettuce and 6 asparagus have one-half of the carbohydrate of 9 cups of raw tomatoes. One cup each of raw tomatoes and raw lettuce has 3 times the carb content of 6 asparagus spears. Find the number of grams in the given portion of size of each vegetable.
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the grams of carbohydrates in a cup of raw lettuce, y for raw asparagus spears, and z for raw tomatoes. Then, we have the system of equations system%28x%2B6y%2Bz=12%2Cx%2B6y=4.5z%2C+x%2Bz=18y%29. Subtracting z from both sides of the first equation, we get x%2B6y=12-z. Subtracting that from the second equation, we get 5.5z=12. Dividing both sides by 5.5 gives z=12%2F5.5=highlight%2824%2F11%29.
If we subtract 18y from both sides of the third equation, we get x-18y%2Bz=0. Subtracting that from the first equation gives 24y=12. Dividing both sides by 24 gives y=highlight%281%2F2%29.
We can plug the values that we found for y and z into the first equation to get x%2B6%2A1%2F2%2B24%2F11=12. Simplifying, we get x%2B3%2B24%2F11=12. We isolate x to get x=12-3-24%2F11=9-24%2F11=99%2F11-24%2F11=highlight%2875%2F11%29.
In conclusion, the solutions are system%28x=75%2F11%2Cy=1%2F2%2Cz=24%2F11%29.
Check: 75%2F11%2B6%2A1%2F2%2B24%2F11=99%2F11%2B3=9%2B3=12
75%2F11%2B6%2A1%2F2=75%2F11%2B3=75%2F11%2B33%2F11=108%2F11=4.5%2A24%2F11=4.5z.
75%2F11%2B24%2F11=99%2F11=9=18%2A1%2F2=18y.