SOLUTION: question 9 Joe has three times as many as Tom, and Tom has four times as many as Mary. Altogether they have 153. How many has each? Mary has ……… Tom has 51 Joe has ……….

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: question 9 Joe has three times as many as Tom, and Tom has four times as many as Mary. Altogether they have 153. How many has each? Mary has ……… Tom has 51 Joe has ……….       Log On


   

Question 873596: question 9
Joe has three times as many as Tom, and Tom has four times as
many as Mary. Altogether they have 153. How many has each?
Mary has ………
Tom has 51
Joe has ……….
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Joe has three times as many as Tom, 
So J = 3T

and Tom has four times as many as Mary.
So T = 4M

Altogether they have 153. 
J+T+M = 153

So we have this system of three equations:

system%28J=3T%2CT=4M%2CJ%2BT%2BM=153%29

Substitute 4M for T in J=3T

J=3T
J=3(4M)
J=12M

12M for J, and 4M for T in J+T+M = 153

12M+4M+M = 153
     17M = 153
       M = 9

Substitute 9 for M in J = 12M

J = 12M
J = 12(9)
J = 108

Substitute 9 for M in T = 4M

T = 4M
T = 4(9)
T = 36

How many has each? 
Joe has 108, Tom has 36, and Mary has 9. 

Edwin