SOLUTION: A type of pasta is made of a blend of quinoa and corn. The pasta company is not disclosing the percentage of each ingredient in the blend but we know that the quinoa in the blend

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: A type of pasta is made of a blend of quinoa and corn. The pasta company is not disclosing the percentage of each ingredient in the blend but we know that the quinoa in the blend       Log On


   

Question 1160612: A type of pasta is made of a blend of quinoa and corn. The pasta company is not disclosing the percentage
of each ingredient in the blend but we know that the quinoa in the blend contains 14.5% protein, and the
corn in the blend contains 2.5% protein. Overall, each 60 gram serving of pasta contains 4 grams of
protein. Model a systems of equations for this problem and solve the system to find how much quinoa and
how much corn is in one serving of the pasta?
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Q+C=60
.145Q+.025C=4
multiply bottom by -40 to eliminate C
-5.8Q-C=-160
add the top
-4.8Q=-100
Q=20.83 gm with 3.021 gm protein
C=39.17 gm corn with 0.979 gm protein

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Let x = grams of quinoa
Let y = grams of corn

Then 0.145x = grams of protein in the quinoa
and 0.025y = grams of protein in the corn

x%2By+=+60 the sample is 60 grams
0.145x%2B0.025y+=+4 the amount of protein is 4 grams

Usually when a system of linear equations has both equations in the form ax+by=c, I would use elimination. But with the ugly coefficients in the second equation, I choose to use substitution.

y+=+60-x
0.145x%2B0.025%2860-x%29+=+4

I'll let you finish from there.

Note that the last equation I show in my work is what would be my starting equation, if the instructions had not said to use a system of equations. Nearly always, solving a problem using a single variable and a single equation is easier and faster than solving a pair of equations in two variables.