Boxes A nad B contain a total of 480 marbles. After 0.25 of the marbles in Box A is taken out and put in Box B, and then 0.5 of the marbles in Box B is taken out and put in A, the number of marblesin Box A becomes 3 times the number of marbles in Box B. What is the number of marbles in Box B at first?
To solve this problem, let's denote the number of marbles in Box A as A and the number of marbles in Box B as B.
We are given that A + B = 480 since the total number of marbles in both boxes is 480.
According to the problem, after taking out 0.25 of the marbles in Box A and moving them to Box B, and then taking out 0.5 of the marbles in Box B and moving them to Box A, the number of marbles in Box A becomes 3 times the number of marbles in Box B.
So, we can set up the following equations:
A - 0.25A + 0.5B = 3(B - 0.5B)
Simplifying this equation, we get:
0.75A + 0.5B = 1.5B
0.75A = 1B
0.75A = B
Now, we know that B = 0.75A.
Substituting this value of B into the equation A + B = 480, we can solve for A:
A + 0.75A = 480
1.75A = 480
A = 480 / 1.75
A ≈ 274.29
Now, we know that B = 0.75A, so:
B = 0.75 * 274.29
B ≈ 205.72
Therefore, the number of marbles in Box B at first is approximately 206.