Question 6347: One serving of green beans contains 1 gram of protein and 4 grams of carbohydrates. One serving of chicken soup contains 3 grams of protein and 9 grams of carbohydrates. The Westdale Diet recommends a lunch of 13 grams of protein and 43 grams of carbohydrates. How many servings of each are necessary to obtain the recommended amounts?
Answer by prince_abubu(198)   (Show Source):
You can put this solution on YOUR website! In this case, we'll let b be the number of servings of beans and s be the number of servings of soup.
The diet requires 13 grams of protein total. So, if the beans have 1 gram of protein per serving, then there will be 1*b grams of protein in b servings of beans. We also need to add up the protein content of the soup. If each soup serving contains 3 grams of protein, then there will be 3*s grams of protein in s servings of soup. And we wanted the total to be 13 grams, so we have 
The diet also requires 43 grams of carbs. If the beans have 4 grams of carbs, there will be 4b grams of carbs in b servings of beans. If the soup has 9 grams of carbs, then there will be 9s grams of carbs in s servings of soup. So our carb total equation will be  .
We now have a system of linear equations. There are several ways to do this, like graphing (and then looking at where the lines meet), vertical addition/subtraction, or substitution. I think it's easier to use substitution because one of the equations (the ) already has a variable by itself, which is the b. We can rearrange that as  . We can then substitute the 13 - 3s for the b in the other equation:
 <--- solving for s will give us the number of soup servings.
 <--- used distributive property
 <--- combined like terms
 <----- So the diet recommended 3 servings of soup.
 <----- We substituted 3 for s in one of the equations. BTW, it doesn't matter which one of the two equations to use. You'll get the same answer. We just chose the first equation because it's easier to work with.
 <---- So the diet recommended 4 servings of soup.
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