SOLUTION: Mother made cupcakes for the church picnic."If I had made 6 more chocolate cupcakes, I would have as many chocolate as I do white and pepermint combined,"said Mother."I have 4 more

Question 117319: Mother made cupcakes for the church picnic."If I had made 6 more chocolate cupcakes, I would have as many chocolate as I do white and pepermint combined,"said Mother."I have 4 more white than peppermint."Altogether she baked 50 cupcakes.How many of each kind did she have?
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Mother made cupcakes for the church picnic."If I had made 6 more chocolate cupcakes, I would have as many chocolate as I do white and pepermint combined,"said Mother."I have 4 more white than peppermint."Altogether she baked 50 cupcakes.How many of each kind did she have?
:
Let c = no. of chocolate c.c.
Let w = no. of whites
Let p = no. of peppermints
:
Write an equation from the statement:
"If I had made 6 more chocolate cupcakes, I would have as many chocolate as I do white and pepermint combined,"
c + 6 = w + p
:
"I have 4 more white than peppermint."
w = p + 4
:
Altogether she baked 50 cupcakes.
c + w + p = 50
:
How many of each kind did she have?
:
Take the 1st equation and replace w with (P+4)
c + 6 = (p+4) + p
Simplify
c + 6 = 2p + 4
c = 2p + 4 - 6
c = 2p - 2
:
In the 3rd equation, replace c with(2p-2) and replace w with (p+4); find p
(2p-2) + (p+4) + p = 50
2p + p + p -2 + 4 = 50
4p + 2 = 50
4p = 50 - 2
p = 48/4
p = 12 peppermint c.c.
:
You can find the other amts using the equations we have here
:
Check solutions in the 3rd equation
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
c = number of chocolate
w = number of white
p = number of pepermint
w + p + c = 50
w + p = c + 6
w = p + 4
add the 1st and 2nd equations
2w + 2p = 56
Substitute w from the 3rd into this result
2(p + 4) + 2p = 56
2p + 8 + 2p = 56
4p = 48
p = 12
There are 12 peppermint
w = p + 4
w = 12 + 4
w = 16
There are 16 white
w + p + c = 50
16 + 12 + c = 50
28 + c = 50
c = 22
There are 22 chocolate
check answer
w + p = c + 6
16 + 12 = 22 + 6
28 = 28
OK
w + p + 4
16 = 12 + 4
16 = 16
OK
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