A certain number has three digits. The sum of the three digits equals 36 times this number. Seven times the left digit plus 9 is equal to 5 times the sum of the two other digits. 8 times the second digit minus 9 is equal to the sum of the first and third.
A woman went into a bank to cash an insurance refund check. By mistake the teller gave her dollars for cents and cents for dollars. She put the money in her purse but accidentally dropped a nickel on the floor. When she got home, she found that she had exactly twice the amount of the check she had cashed. She didn't have any money in her wallet before going to the bank. What was the exact amount of that check?
The amount must have been $31.63. She received $63.31. After she dropped a nickel there would remain the sum of $63.26, which is twice the amount of the check.
An officer wishing to arrange his men in a solid square found by his first arrangement that he had 39 men left over. He then started increasing the number of men on a side by one, but found that 50 additional men would be needed to complete a new square.
How many men did the officer have?
The officer had 1975 men. When he formed a square measuring 44 by 44, he had 39 men over. When he tried to form a square 45 x 45, he was 50 men short.