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
<pre>Let amount received by Ali, Bala, and Charlie, be A, B, and C, respectively
Then: {{{matrix(1,5, A/B = 7/6, "=====>", 6A = 7B, "====>", A = 7B/6)}}} ------ eq (i)
Also, {{{matrix(1,5, B/C = 4/5, "====>", 4C = 5B, "====>", C = 5B/4)}}} ------- eq (ii)
We then get: {{{B + 7B/6 + 5B/4 = 328}}}
12B + 14B + 15B = 3,936 ------- Multiplying by LCD, 12
41B = 3,936
B, or amount Bala received = {{{matrix(1,3, "3,936"/41, or, 96 )}}}

{{{A = 7(96)/6}}} ------- Substituting 96 for B in eq (i)
A, or amount received by Ali = {{{matrix(1,3, 7(16), or, 112)}}}
 
{{{C = 5(96)/4}}} ------- Substituting 96 for B in eq (ii)
C, or amount received by Charlie = {{{matrix(1,3, 5(24), or, 120)}}}

{{{highlight_green(matrix(3,4, Amount, Ali, "received:", 112, Amount, Bala, "received:", 96, Amount, Charlie, "received:", 120))}}}</pre>