document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #832995 by Shin123(626)\"\" \"About 
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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\".
\n" ); document.write( "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\".
\n" ); document.write( "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\".
\n" ); document.write( "In conclusion, the solutions are \"system%28x=75%2F11%2Cy=1%2F2%2Cz=24%2F11%29\".
\n" ); document.write( "Check: \"75%2F11%2B6%2A1%2F2%2B24%2F11=99%2F11%2B3=9%2B3=12\"
\n" ); document.write( "\"75%2F11%2B6%2A1%2F2=75%2F11%2B3=75%2F11%2B33%2F11=108%2F11=4.5%2A24%2F11=4.5z\".
\n" ); document.write( "\"75%2F11%2B24%2F11=99%2F11=9=18%2A1%2F2=18y\". \n" ); document.write( "
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