SOLUTION: Katy, Mary and Emma make 43 cakes in total. The number of cakes that Mary makes is 7 less than that Katy makes and 3 less than three times the number of cakes that Emma makes. Find

Algebra ->  Equations -> SOLUTION: Katy, Mary and Emma make 43 cakes in total. The number of cakes that Mary makes is 7 less than that Katy makes and 3 less than three times the number of cakes that Emma makes. Find      Log On


   

Question 1204895: Katy, Mary and Emma make 43 cakes in total. The number of cakes that Mary makes is 7 less than that Katy makes and 3 less than three times the number of cakes that Emma makes. Find the number of cakes that each of them makes.
Answer by mananth(16946) About Me  (Show Source):
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Katy, Mary and Emma make 43 cakes in total. The number of cakes that Mary makes is 7 less than that Katy makes and 3 less than three times the number of cakes that Emma makes. Find the number of cakes that each of them makes.
E = cakes made by E
K= cakes made by Katy
M cakes made by Emma
The total number of cakes is 43
E +K+M=43
The number of cakes that Mary is 3 less than three times the number of cakes that Emma makes
M= 3E-3
E= (M+3)/3
The number of cakes that Mary makes is 7 less than that Katy makes
M=K-7
K= M+7
Mary =M
M+K+E=43
M+M+7+ (M+3)/3 =43
Multiply by 3
3M+3M+21+M+3= 129
7M+24=129
7M = 129-24
7M = 105
divide by 7
M= 15
M=K-7
K= M+7 = 22
E=(M+3)/3= (15+3)/3= 6

Emma makes 6
Katy makes 22
Mary makes 15


6+22+15= 43