Answer:
Machine A has 8144 tokens, machine B has 4072 tokens and machine C has 6108 tokens.
Step-by-step explanation:
Let call: X the number of tokens that machine A has, Y the number of tokens that machine B has and Z the number of tokens that machine C has.
From the sentence: He puts twice the number in machine A as in machine B, we can formulate the equation 1 as:
X = 2*Y
Solving for Y we can write the equation 1 as:
Y = X/2
From the sentence: in machine C , he puts 3/4 of what he put in machine A, we can formulate the equation 2 as:
Z = (3/4)*X
And from the sentence the total amount of tokens was 18324. we can formulate the equation 3 as:
X + Y + Z = 18324
So, if we replace the Y by X/2 and Z by (3/4)X on equation 3 and solve for X, we get:
X + Y + Z = 18324
X + X/2 + (3/4)X = 18324
(9/4)X=18324
X = 18324*(4/9)
X = 8144
Then, replacing this value on equation 1 and 2 to find Y and Z respectively, we get:
Y = X/2 = 8144/2 = 4071
Z = (3/4)*X = (3/4)*4071 = 6108
So, machine A has 8144 tokens, machine B has 4072 tokens and machine C has 6108 tokens.
