There were 415 marbles in tins A, B, C and D altogether. 10 marbles were taken out of Tin A while 18 more marbles were put into Tin B. Half of the number of marbles in Tin C were removed and the number of marbles in Tin D was doubled. There is an equal number of marbles in each tin now. Find the number of marbles in tins A and C
Question
There were 415 marbles in tins A, B, C and D altogether. 10 marbles were taken out of Tin A while 18 more marbles were put into Tin B. Half of the number of marbles in Tin C were removed and the number of marbles in Tin D was doubled. There is an equal number of marbles in each tin now. Find the number of marbles in tins A and C
Solution
Let's denote the initial number of marbles in each tin as follows: A for Tin A, B for Tin B, C for Tin C, and D for Tin D.
From the problem, we know that:
A + B + C + D = 415 (equation 1)
After the changes, we know that:
A - 10 = B + 18 = C/2 = 2D (equation 2)
Since all tins have the same number of marbles after the changes, we can say that:
A - 10 = B + 18 = C/2 = 2D (equation 3)
From equation 3, we can express B, C, and D in terms of A:
B = A - 28 C = 2A - 20 D = (A - 10) / 2
Substitute B, C, and D in equation 1:
A + (A - 28) + (2A - 20) + ((A - 10) / 2) = 415 4.5A - 58 = 415 4.5A = 473 A = 473 / 4.5 A = 105
Substitute A = 105 in C = 2A - 20:
C = 2*105 - 20 C = 190
So, initially, there were 105 marbles in Tin A and 190 marbles in Tin C.
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