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.

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