SOLUTION: Please help me with this problem. How can you relate three variables with 2 different situations? If it takes 12 eggs to make 2 cakes and 1 dozen cookies, and 19 eggs to make 3

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Question 134989: Please help me with this problem. How can you relate three variables with 2 different situations?
If it takes 12 eggs to make 2 cakes and 1 dozen cookies, and 19 eggs to make 3 cakes and 2 dozen cookies, how many eggs does it take to make one cake?
Found 2 solutions by stanbon, rajagopalan:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
If it takes 12 eggs to make 2 cakes and 1 dozen cookies, and 19 eggs to make 3 cakes and 2 dozen cookies, how many eggs does it take to make one cake?
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EQUATIONS:
2c+d = 12e
3c+2d = 19e
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Subtract 1st from 2nd to get:
c+d = 7e
c = 7e-d
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Substitute to solve for "d"
2(7e-d) + d = 12e
14e-d = 12e
e = 2e
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Therefore one cake = 7e-2e = 5eggs
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Cheers,
Stan H.

Answer by rajagopalan(174) (Show Source):
You can put this solution on YOUR website!
It is only 2 independat varables ( cake, cokies) and 1 dependant variable (egg).
the problem can be constructed as thus:
let no of eggs needed for a cake =x
let no of eggs needed for a cookie =y
then
2x+12y=12....eq1
3x+24y=19....eq2
multiply first eq with 2 and the second eq with 3
6x+36y=36...eq 3
6x+48y=38...eq 4
subtract eq 3 from 4
we get
12y=2
y=2/12=1/6
substitute this value in eq 1
2x+(12/6)=12
2x=12-2
2x=10
x=5
No of eggs for a cake = 5
okay