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?

Question

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 1

To solve this problem, let's break it down step by step:

Step 1: Let's assume the original number of dimes in Box A is "x."

Step 2: According to the first statement, if 25 dimes were moved from Box A to Box B, the number of dimes in each box would be equal. This means that after the transfer, both Box A and Box B would have (x - 25) dimes.

Step 3: Next, using the second statement, 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. This can be written as:

(x - 25 + 100) / (x - 25) = 7/2

Step 4: Simplify the equation:

(x + 75) / (x - 25) = 7/2

Cross multiply:

2(x + 75) = 7(x - 25)

Step 5: Expand and solve the equation:

2x + 150 = 7x - 175

-5x = -325

x = 65

Therefore, the original number of dimes in Box A was 65.

Answer 2

Let's solve this step by step:

Let's assume the original number of dimes in Box A is x.

Step 1: If 25 dimes were moved from Box A to Box B, the new number of dimes in Box A would be x-25, and the new number of dimes in Box B would be 25.

Step 2: According to the given information, when 100 dimes were moved from Box B to Box A, the ratio of dimes in Box A to Box B became 7:2.

So, the new number of dimes in Box A is (x-25)+100 = x+75, and the new number of dimes in Box B is 25-100 = -75.

Step 3: We can set up a ratio equation based on the given information:

(x+75)/(-75) = 7/2.

Cross-multiplying and simplifying, we get:

2(x+75) = 7(-75).

2x+150 = -525.

Step 4: Solving for x:

2x = -525 - 150.

2x = -675.

x = -337.5.

Since the number of dimes cannot be negative, it's not possible to have a negative number of dimes in Box A. Therefore, there seems to be an error or inconsistency in the given information or problem statement.

Please check the problem statement or provide additional information to proceed further.

Answer 3

A - 25 = B + 25

... A - 50 = B

7(B - 100) = 2(A + 100)
... 7 B - 700 = 2 A + 200
... 7 B = 2 A + 900

substituting
... 7(A - 50) = 2 A + 900
... 7 A - 350 = 2 A + 900
... 5 A = 1250 ... A = 250