You collect rents from your tenants in the following amounts: $565, $600, $650, $650, $723, $725, $715, $800 and $900. You get a frantic call from the 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 is (are) missing?

1 answer

To identify which rent might be missing, we need to first calculate the total of the collected rents.

Here are the rent amounts:

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

Now we will add these amounts together:

\[ 565 + 600 + 650 + 650 + 723 + 725 + 715 + 800 + 900 = 7,838 \]

The total amount of rents collected is $7,838.

According to the bank reconciliation, only $5,038 was deposited.

To find out how much rent is missing, we will subtract the deposited amount from the total rent collected:

\[ 7,838 - 5,038 = 2,800 \]

Thus, we are missing a total of $2,800 from the deposit.

Next, we will check which combinations of the rents could sum up to $2,800. However, since the rents you collected are not very high on average, it’s unlikely that any single rent amount is missing – rather, it will probably involve the combination of some of them.

Let’s analyze the larger rent amounts since they are more likely to sum closely to $2,800:

If we sum all rents but the highest ones and explore combinations:

  • Ignoring $900: \[ 565 + 600 + 650 + 650 + 723 + 725 + 715 + 800 = 5,733 \quad \text{(missing: $2,105)} \]
  • Ignoring $800: \[ 565 + 600 + 650 + 650 + 723 + 725 + 715 + 900 = 6,033 \quad \text{(missing: $1,805)} \]
  • Ignoring both $800 and $900: \[ 565 + 600 + 650 + 650 + 723 + 725 + 715 = 4,938 \quad \text{(missing: $2,900)} \]

Attempting combinations can be complicated, but since the largest rent is only $900.

If we were to guess, it may be that the rent amount of $800 or $900 was mistakenly left out. Let’s exclude two amounts $900 and $725, we check:

\[ 565 + 600 + 650 + 650 + 723 + 715 = 3,613 \quad \text{(missing: $2,225)} \]

Upon checking systematically, you find identifying smaller gaps might help yield quicker results.

Summarily, if $800 or $900 was unaccounted in the further scenarios. In summary, approximating calculations conclude towards neglect over higher ranges like $800 or $900 being most probable to yield missing amounts.