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

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) (Show Source): You can put this solution on YOUR website!
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

RELATED QUESTIONS
Sheena’s Bakery makes and sells cookies and cakes. It costs the store Php580 to buy the (answered by ikleyn)

Amy baked 18 more banana cakes than butter cakes. After giving away 35 cakes of each... (answered by ikleyn)

9. A bakery makes a profit of $10 for each cake sold and $5 for each pie sold. They need (answered by jorel1380)

Abu came out of the bakery shop after spending RM 320 on carrot cakes, cheese cakes and... (answered by robertb)

Ailing bought 3 similar big cakes and 4 similar small cakes . The total mass of the 7... (answered by josgarithmetic,MathTherapy)

if a recipe for cake calls 2 1/2 cups of flour and Mary wishes to make three such cakes... (answered by jim_thompson5910)

Tom is shorter than Mary and older than Joe. Mary is shorter than Joe but older than Tom. (answered by ankor@dixie-net.com)

Hi joan sold cookies cakes and muffins in chocolate or butter flavor. She sold 140 more... (answered by josgarithmetic)

James bought a packet of flour to make cakes. He used an equal amount of flour for each... (answered by MathLover1)