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You collect rents from your tenants. In the following amounts 565, 600, 650, 650, 723, 725, 715, 800 and 900. You get in a frantic call from an accounting department that there was an error in the bank deposit you made. The bank reconciliation reveals that 5,038 was deposited. Which rents do you think that are missing

1 answer

To find the missing rents, we first need to calculate the total of the rents collected. Here are the amounts:

  • 565
  • 600
  • 650
  • 650
  • 723
  • 725
  • 715
  • 800
  • 900

Let's add these amounts:

\[ 565 + 600 + 650 + 650 + 723 + 725 + 715 + 800 + 900 = 5,737 \]

Now, we know that the total deposited amount was $5,038. To find out what is missing, we can subtract the deposited amount from the total collected:

\[ 5,737 - 5,038 = 699 \]

This means that there is a total of $699 missing from the deposit.

Next, we need to find which combination of the rents adds up to $699. From the rent amounts provided, let's examine the options:

The rents available are:

  • 565
  • 600
  • 650
  • 650
  • 723
  • 725
  • 715
  • 800
  • 900

Since we need to find rents that add up to $699, let's analyze possible combinations:

  1. 650 + 650 = 1300 (too high)
  2. 800 + 900 = 1700 (too high)
  3. 723 + any remaining amount will be too high (minimum additional amount would be 650).
  4. 600 + 650 = 1250 (too high)
  5. 715 + 800 = 1515 (too high)

Based on the amounts available, let's look for pairs starting from the highest:

  • 650 + 725 = 1375 (too high)
  • 650 + 715 = 1365 (too high)
  • 600 + 715 = 1315 (too high)
  • 565 + 715 = 1280 (too high)
  • Continue checking combinations...

Finally, we find that:

  • 650 + 723 = 1373 (too high)

Let's check different combinations until we exhaust them.

However, a more efficient approach is to check the rents less than 699.

It looks like the 665 and 725 do not help, so we need to conclude the possible missing rent could primarily depend on the values of 600, 650, 723, etc.

Checking all combinations manually, we can conclude:

  1. The combination that matches up to $699 could be either
    • 650 (selected once)
    • 600
    • 565

The final combinations yielding up to 699 are thus, unfortunately will depend further on unique pairs or multiples of tenants skipped.

In sum, the amounts missing from total deposited could have potentially been a combination of either 650 or 600 (as noted).

In the end: Upon verification, the actual only value combination that leaves us stays unexplained, as sums of quarters are only found from bound to explore upwards:

Missing Amount = 699 (most likely $650 & $600 or combination thereof).