SOLUTION: Matt has 50 cookies to give to his class. There were three kinds of cookies; chocolate chip, M&M, and sugar cookies. There are twice as many sugar cookies as chocolate chip cookies

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Question 212822: Matt has 50 cookies to give to his class. There were three kinds of cookies; chocolate chip, M&M, and sugar cookies. There are twice as many sugar cookies as chocolate chip cookies and two more M&M cookies than there are chocolate chip cookies. Write the system and find out how many of each type of cookie he brought.
Answer by aggie_tutor(13) About Me  (Show Source):
You can put this solution on YOUR website!
50 = c + m + s
where c = chocochip, m = M&M and s = sugar.
Let's get everything in terms of one of the cookies to simplify.
Sugar cookies twice as many as chocochip: s+=+2%2Ac
Two more M&M than chocochip: m+=+c+%2B+2
Now express total just in terms of chocochips cookies:
50+=+c+%2B+s+%2B+m
50+=+c+%2B+%282%2Ac%29+%2B+%28c%2B2%29
50+=+c+%2B+2c+%2B+c+%2B+2
Simplify :
50+=+4c+%2B+2
50+%28-2%29+=+4c+%2B+2+%28-2%29
48+=+4c
48%2F4+=+c
c+=+12
Now we know there were 12 chocochip. Plug in this number to find the others.
s+=+2%2Ac+=+2%2A12+=+24 Sugar cookies
m+=+c%2B2+=+12%2B2+=+14 M&M cookies
Check your work by adding them all up:
24 + 14 + 12 = 50