Question

Early one morning, Sandy took out one-half of the coins from her coin bank, and in the evening, she put in 20 coins. The next morning, she took out one-third of the coins in the bank, and that evening, she put in 4 coins. The next morning, she took out one-half of the coins in the bank, leaving 15 coins. How many coins were in the bank to begin with?

a) 60
b) 75
c) 90
d) 105

Answer 1

Working backward from the final number of coins Sandy had, it seems she started with 38 coins in the bank. The given answer choices do not match this number, suggesting there might be an error in the question or the answer options.

Step-by-step explanation:

We need to find out how many coins were in Sandy's bank initially. Let's work backward from what we know. After the last action, Sandy is left with 15 coins. This happened after she took out half, so before that, she must have had 30 coins (since 15 is half of 30).

She added 4 coins the evening before, which means she had 26 coins before adding the 4. This means she took out one-third in the morning, so she would have had 39 coins before taking out one-third because 26 is two-thirds of 39.

The previous evening, Sandy added 20 coins. This means that, before adding 20, she had 19 coins (39 - 20). Since that was after taking out half in the morning, she should have had 38 coins at the beginning of the first day (since 19 is half of 38).

Therefore, the answer is 38 coins. However, none of the given options (a) 60, (b) 75, (c) 90, or (d) 105, matches 38 coins. There might be a mistake in either the question or the provided options.