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

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) (Show Source): You can put this solution on YOUR website!
Let be the grams of carbohydrates in a cup of raw lettuce, for raw asparagus spears, and for raw tomatoes. Then, we have the system of equations . Subtracting from both sides of the first equation, we get . Subtracting that from the second equation, we get . Dividing both sides by gives .
If we subtract from both sides of the third equation, we get . Subtracting that from the first equation gives . Dividing both sides by 24 gives .
We can plug the values that we found for and into the first equation to get . Simplifying, we get . We isolate to get .
In conclusion, the solutions are .
Check:
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