Algebra

Algebra is a broad branch of mathematics that uses symbols (usually letters) to represent numbers and to state rules and relationships. It involves manipulating expressions, solving equations and inequalities, and studying functions and structures. Questions cover a wide range of these topics.

Algebraic Techniques Equations Inequalities Word Problems Sequences

  • BUYING PRESENTS

    "Whom do you think I met in town last week, Brother William?" said Uncle Benjamin. "That old skinflint Jorkins. His family had been taking him around buying Christmas presents. He said to me, 'Why cannot the government abolish Christmas, and make the giving of presents punishable by law? I came out this morning with a certain amount of money in my pocket, and I find I have spent just half of it. In fact, if you will believe me, I take home just as many shillings as I had pounds, and half as many pounds as I had shillings. It is monstrous!'" Can you say exactly how much money Jorkins had spent on those presents? Sources:

  • THE CYCLISTS' FEAST

    'Twas last Bank Holiday, so I've been told,
    Some cyclists rode abroad in glorious weather.
    Resting at noon within a tavern old,
    They all agreed to have a feast together.
    "Put it all in one bill, mine host," they said,
    "For every man an equal share will pay."
    The bill was promptly on the table laid,
    And four pounds was the reckoning that day.
    But, sad to state, when they prepared to square,
    'Twas found that two had sneaked outside and fled.
    So, for two shillings more than his due share
    Each honest man who had remained was bled.
    They settled later with those rogues, no doubt.
    How many were they when they first set out?
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  • A QUEER THING IN MONEY

    It will be found that £`66, 6`s. `6`d. equals `15,918` pence. Now, the four `6`'s added together make `24`, and the figures in `15,918` also add to `24`. It is a curious fact that there is only one other sum of money, in pounds, shillings, and pence (all similarly repetitions of one figure), of which the digits shall add up the same as the digits of the amount in pence. What is the other sum of money? Sources:

  • SQUARE MONEY

    "This is queer," said McCrank to his friend. "Twopence added to twopence is fourpence, and twopence multiplied by twopence is also fourpence." Of course, he was wrong in thinking you can multiply money by money. The multiplier must be regarded as an abstract number. It is true that two feet multiplied by two feet will make four square feet. Similarly, two pence multiplied by two pence will produce four square pence! And it will perplex the reader to say what a "square penny" is. But we will assume for the purposes of our puzzle that twopence multiplied by twopence is fourpence. Now, what two amounts of money will produce the next smallest possible result, the same in both cases, when added or multiplied in this manner? The two amounts need not be alike, but they must be those that can be paid in current coins of the realm. Sources:

  • POCKET MONEY

    What is the largest sum of money—all in current silver coins and no four-shilling piece—that I could have in my pocket without being able to give change for a half-sovereign? Sources:

  • THE PUZZLING MONEY-BOXES

    Four brothers—named John, William, Charles, and Thomas—had each a money-box. The boxes were all given to them on the same day, and they at once put what money they had into them; only, as the boxes were not very large, they first changed the money into as few coins as possible. After they had done this, they told one another how much money they had saved, and it was found that if John had had `2`s. more in his box than at present, if William had had `2`s. less, if Charles had had twice as much, and if Thomas had had half as much, they would all have had exactly the same amount.Now, when I add that all four boxes together contained `45`s., and that there were only six coins in all in them, it becomes an entertaining puzzle to discover just what coins were in each box. Sources:

  • THE MARKET WOMEN

    A number of market women sold their various products at a certain price per pound (different in every case), and each received the same amount—`2`s. `2`½d. What is the greatest number of women there could have been? The price per pound in every case must be such as could be paid in current money. Sources:

  • THE NEW YEAR'S EVE SUPPERS

    The proprietor of a small London café has given me some interesting figures. He says that the ladies who come alone to his place for refreshment spend each on an average eighteenpence, that the unaccompanied men spend half a crown each, and that when a gentleman brings in a lady he spends half a guinea. On New Year's Eve he supplied suppers to twenty-five persons, and took five pounds in all. Now, assuming his averages to have held good in every case, how was his company made up on that occasion? Of course, only single gentlemen, single ladies, and pairs (a lady and gentleman) can be supposed to have been present, as we are not considering larger parties. Sources:

  • BEEF AND SAUSAGES

    "A neighbour of mine," said Aunt Jane, "bought a certain quantity of beef at two shillings a pound, and the same quantity of sausages at eighteenpence a pound. I pointed out to her that if she had divided the same money equally between beef and sausages she would have gained two pounds in the total weight. Can you tell me exactly how much she spent?"

    "Of course, it is no business of mine," said Mrs. Sunniborne; "but a lady who could pay such prices must be somewhat inexperienced in domestic economy."

    "I quite agree, my dear," Aunt Jane replied, "but you see that is not the precise point under discussion, any more than the name and morals of the tradesman."

    Sources:

  • A DEAL IN APPLES

    I paid a man a shilling for some apples, but they were so small that I made him throw in two extra apples. I find that made them cost just a penny a dozen less than the first price he asked. How many apples did I get for my shilling?
    Topics:
    Algebra -> Word Problems
    Sources: