SOLUTION: 328 marbles are to be divided among ali, bala and charlie. the number of marbles recieved by ali and bala are in the ratio of 7:6 and recieved by bala and charlie are in the ratio

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 328 marbles are to be divided among ali, bala and charlie. the number of marbles recieved by ali and bala are in the ratio of 7:6 and recieved by bala and charlie are in the ratio      Log On


   

Question 1065009: 328 marbles are to be divided among ali, bala and charlie. the number of marbles recieved by ali and bala are in the ratio of 7:6 and recieved by bala and charlie are in the ratio of 4:5 . Calculate the number of marbles recieved by each
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39621) About Me  (Show Source):
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This is for getting the ratios only... 
ali   :   bala   :   charlie
7     :    6     :    c
a     :    4     :    5



The 6 and the 4 parts in the different ratio list mean the way the two ratios are related is 3 to 2.
Find a using 2%2F3 of 7.
Find c using 3%2F2 of 5.
ali   :   bala   :   charlie
7     :    6     :    7.5
4&2/3 :    4     :    5


The two ratios are the same. 

7 : 6 : 7.5
same as 
4%262%2F3 : 4 : 5

Answer by MathTherapy(10555) About Me  (Show Source):
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328 marbles are to be divided among ali, bala and charlie. the number of marbles recieved by ali and bala are in the ratio of 7:6 and recieved by bala and charlie are in the ratio of 4:5 . Calculate the number of marbles recieved by each
Let amount received by Ali, Bala, and Charlie, be A, B, and C, respectively
Then:  ------ eq (i)
Also,  ------- eq (ii)
We then get: B+%2B+7B%2F6+%2B+5B%2F4+=+328
12B + 14B + 15B = 3,936 ------- Multiplying by LCD, 12
41B = 3,936
B, or amount Bala received = matrix%281%2C3%2C+%223%2C936%22%2F41%2C+or%2C+96+%29

A+=+7%2896%29%2F6 ------- Substituting 96 for B in eq (i)
A, or amount received by Ali = matrix%281%2C3%2C+7%2816%29%2C+or%2C+112%29
 
C+=+5%2896%29%2F4 ------- Substituting 96 for B in eq (ii)
C, or amount received by Charlie = matrix%281%2C3%2C+5%2824%29%2C+or%2C+120%29

Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
328 marbles are to be divided among ali, bala and charlie. the number of marbles recieved by ali and bala are in the ratio of 7:6
and recieved by bala and charlie are in the ratio of 4:5 . Calculate the number of marbles recieved by each
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let A be the number of marbles Ali received.

Then Bala received is %286%2F7%29%2AA.

Then Charlie received %285%2F4%29%2A%286%2F7%29%2AA = 30%2F28%29%2AA = %2815%2F14%29%2AA.

The equation for the total is 

A+%2B+%286%2F7%29%2AA+%2B+%2815%2F14%29%2AA = 328.

A%2A%281+%2B+6%2F7+%2B+15%2F14%29 = 328,

A%2A%28%2814+%2B+12+%2B+15%29%2F14%29 = 328,

A%2A%2841%2F14%29 = 328  --->  A = %28328%2A14%29%2F41 = 112.

Then B = %286%2F7%29%2A112 = 96,  C = %2815%2F14%29%2A112 = 120.

Check.  112 + 96 + 120 = 328.

Answer.  A= 112,  B= 96,  C= 120.