Mistake At The ATM

(Maths Problem)

NB. Student answers are in red.

Part 1: Missing Money - The Basic Facts

On Wednesday morning Wesley, the bank auditor, checks a record of deposits and withdrawals at the ATM machine and night deposit box from the previous day and finds that there has been a mix-up.  This is what he finds:

 

ATM opening balance	$15 500.00
deposits	4 572.18
withdrawals	7 900.00
balance should have been	$12172.18ü

When he actually counted the money, he found that he had:

cheques	$3 959.23
cash	3 212.95
total	$7172.18ü

 

He is missing

$5000ü

Wesley begins investigating to see if he can discover where the mistake has been made.  He calls the police and together they decide to investigate the most likely suspects.  They are Adam Dogood, Barney Bust, Camille Cash, Miss Take and Mark Down.

Part 2: Bank Times

Wesley figures that the extra money was distributed between one o'clock and two o'clock Tuesday afternoon, so the police question the five suspects about their whereabouts.  Use the police report to work out the time each person visited the ATM machine.

1. Adam Dogood went to the bank during his lunch hour.  He got off work at 1:00p.m., went to the post office and then to the bank.  It is a ten minute walk between his workplace and the post office and a 15 minute walk between the post office and the bank.

Adam visited the bank at

1:25p.m.ü

2.Barney Bust visited the ATM and then drove to the car lot to pick up his new car at 2:00p.m. The car lot is a 15 minute drive from the bank.

Barney visited the bank at

1:45p.m.ü

3. Camille Cash left her hair dresser at 1:00p.m. and then did several errands, including going to the bank, between that time and 4:00p.m. when she arrived at the community centre for her volunteer work.

Camille visited the bank at

2:30p.m.x How do you know this? She visited some time between 1 and 4, there is no other information.

4. Miss Take visited the ATM before going to her karate lesson at 2:00p.m. It is a 20 minute drive between the bank and the karate studio.

Miss Take visited the bank at

1:40pmü

5. Mark Down visited the bank twice, once at 2:15p.m. and once half an hour earlier.

Mark visited the bank at

1:45p.m. and 2:15p.m.ü

 

Can any suspects be eliminated?

No I can't eliminate anyone.ü

Part 3: The Investigation

These are the records for the five people who made withdrawals at the ATM on Tuesday afternoon:

opening balance		amount withdrawn	balance should be
Adam Dogood	$875.50	$200.00	$675.50ü
Barney Bust	$659.20	$550.00	$109.20ü
Camille Cash	$942.67	$110.00	$832.67ü
Miss Take	$296.40	$75.00	$221.40ü
Mark Down	$3 469.50	$125.00	$3344.50ü

A search of the suspects' homes on Wednesday afternoon reveals the following facts about the five suspects:

1. Adam Dogood has a bank balance of $675.50, $150.00 in his wallet, and $459.00 stashed in a sock under his bed.

2. Barney Bust has a bank account that shows a balance of $109.20, $27.50 in his wallet, and a new car in the garage with 252 kilometres on the odometer.

3. Camille Cash has $832.67 in the bank, $47.80 in the cookie jar, and receipts for a new big screen television and a stereo system.

4. Miss Take has $1 471.80 in the bank, and $352.60 in her purse.

5. Mark Down has $8 344.50 in the bank, a deposit slip for $5 000.00 dated Wednesday morning, and $18.55 in coins in a piggy bank.

Based on the bank records and the results from the search warrants, can any suspects be eliminated? Why?

Mark Down again because he has $5,000 that came from Leon's coins. He has a receipt. You don't actually know this yet!

Part 4: Additional Evidence

While the police are doing their search, they collect some evidence that they will take back to the station to compare with all the other evidence. Each piece of evidence is numbered. Finish the sequences and use the last number of each sequence to match each piece of evidence with the correct suspect.

 

Mark Down	150	140	145	135	140	130	135	125ü	130ü	120ü
Barney Bust	1	2	3	5	8	13	21	34	55ü	89ü	144ü
Camille Cash	3	6	8	16	18	36	38	76	78ü	156ü	158ü
Miss Take	1	2	4	5	16	32	64	128ü	256ü	512ü

Evidence

144 - receipt for a cash payment of $500 to Buy Rights Cars on Tuesday afternoon.

158 - charge slip from Tom's TVs and More for $2 346 that shows a down payment of $100 paid in cash.

120 - receipt from Leon's Coins for $5 000.00 for the sale of two rare coins.

512 - a key to a safe deposit box that contains a deposit slip for $1 250.40 dated Wednesday morning and $3 397.00 in cash.

Who would you charge with the crime and why?

Miss Take because she has enough money to equal $5,000 altogether with all the evidence shown. ü

  Taken from The Loose Caboose Maths Mysteries (Dandy Lion 1997)