If 25 dimes were moved from Box A to Box B, there would be an equal number of dimes in both boxes. If 100 dimes were moved from Box B to Box A, the ratio of dimes in Box A to Box B would be 7:2.
What was the original number of dimes in Box A?
Answer (2)
Calculating the Original Number of Dimes in Box A
Let's denote the original amount of dimes in Box A as A and in Box B as B. If moving 25 dimes from Box A to Box B results in an equal number of dimes in both boxes, we can express this as A - 25 = B + 25.
Simplifying this equation gives us A - B = 50. Now, if 100 dimes are moved from Box B to Box A, the ratio of dimes in Box A to Box B is 7:2. In terms of the dimes, it can be written as (A + 100)/(B - 100) = 7/2.
To find the original number of dimes in Box A, we solve these two equations simultaneously. Multiplying both sides of the ratio equation by 2(B - 100) to clear the fractions, we get 2A + 200 = 7B - 700.
Substituting A - B = 50 into this equation gives us 2(50 + B) + 200 = 7B - 700. Solving for B, we find that B = 300. We then substitute B into A - B = 50 to find that A = 350.
Therefore, the original number of dimes in Box A was 350.
The original number of dimes in Box A was 250. This was determined by setting up two equations based on the transfer of dimes and solving them simultaneously. The calculations were based on the given conditions of equal quantities and ratios after movements of dimes.
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