On a certain day, there were 104 pennies in jar A and 20 pennies in jar B. On each subsequent day, 3 pennies were removed from jar A and 4 pennies were added to jar B until the jars had the same number of pennies. On how many days were pennies removed from jar A?

Rationale

It took 12 days for the number of pennies in jar A and jar B to be equal.

Initially, jar A contains 104 pennies and jar B has 20 pennies. Each day, 3 pennies are removed from jar A and 4 pennies are added to jar B, resulting in a daily change of 7 pennies between the two jars. Thus, it takes 12 days for the two jars to equalize at 64 pennies each.

A (8) YOUR ANSWER

If 8 days were taken, jar A would have 104 - (3 * 8) = 88 pennies, and jar B would have 20 + (4 * 8) = 52 pennies. The difference of 36 pennies would still exist, indicating that the jars would not be equal yet.

B (10) YOUR ANSWER

If 10 days were taken, jar A would have 104 - (3 * 10) = 74 pennies, while jar B would have 20 + (4 * 10) = 60 pennies. The difference of 14 pennies would remain, illustrating that the jars still do not contain an equal number.

C (12) CORRECT

After 12 days, jar A would have 104 - (3 * 12) = 64 pennies, and jar B would have 20 + (4 * 12) = 64 pennies. The jars would be equal with 64 pennies each, confirming that 12 days is indeed the correct answer.

D (14) YOUR ANSWER

If 14 days were taken, jar A would have 104 - (3 * 14) = 58 pennies, and jar B would have 20 + (4 * 14) = 76 pennies. The difference of 18 pennies indicates that this option is incorrect, as the jars would not be equal.

E (16) YOUR ANSWER

If 16 days were taken, jar A would have 104 - (3 * 16) = 56 pennies, and jar B would have 20 + (4 * 16) = 84 pennies. The jars would differ by 28 pennies, confirming that this scenario is also incorrect.

Conclusion

The process of removing and adding pennies leads to their equalization after 12 days, resulting in each jar containing 64 pennies. The calculations for each incorrect option demonstrate that they do not yield the same amount in both jars, thereby confirming that 12 days is the only viable solution to achieve equality.

On a certain day, there were 104 pennies in jar A and 20 pennies in jar B. On each subsequent day, 3 pennies were removed from jar A and 4 pennies were added to jar B until the jars had the same number of pennies. On how many days were pennies removed from jar A?

It took 12 days for the number of pennies in jar A and jar B to be equal.

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