Algebra, Word Problems

Word problems present mathematical challenges in a narrative or real-world context. Solving them requires translating the text into mathematical equations or expressions and then applying appropriate mathematical techniques. These can span arithmetic, algebra, geometry, etc.

Motion Problems Solving Word Problems "From the End" / Working Backwards

  • A POST-OFFICE PERPLEXITY

    In every business of life we are occasionally perplexed by some chance question that for the moment staggers us. I quite pitied a young lady in a branch post-office when a gentleman entered and deposited a crown on the counter with this request: "Please give me some twopenny stamps, six times as many penny stamps, and make up the rest of the money in twopence-halfpenny stamps." For a moment she seemed bewildered, then her brain cleared, and with a smile she handed over stamps in exact fulfilment of the order. How long would it have taken you to think it out? Sources:

  • YOUTHFUL PRECOCITY

    The precocity of some youths is surprising. One is disposed to say on occasion, "That boy of yours is a genius, and he is certain to do great things when he grows up;" but past experience has taught us that he invariably becomes quite an ordinary citizen. It is so often the case, on the contrary, that the dull boy becomes a great man. You never can tell. Nature loves to present to us these queer paradoxes. It is well known that those wonderful "lightning calculators," who now and again surprise the world by their feats, lose all their mysterious powers directly they are taught the elementary rules of arithmetic.

    A boy who was demolishing a choice banana was approached by a young friend, who, regarding him with envious eyes, asked, "How much did you pay for that banana, Fred?" The prompt answer was quite remarkable in its way: "The man what I bought it of receives just half as many sixpences for sixteen dozen dozen bananas as he gives bananas for a fiver."

    Now, how long will it take the reader to say correctly just how much Fred paid for his rare and refreshing fruit?

    Sources:

  • AT A CATTLE MARKET

    Three countrymen met at a cattle market. "Look here," said Hodge to Jakes, "I'll give you six of my pigs for one of your horses, and then you'll have twice as many animals here as I've got." "If that's your way of doing business," said Durrant to Hodge, "I'll give you fourteen of my sheep for a horse, and then you'll have three times as many animals as I." "Well, I'll go better than that," said Jakes to Durrant; "I'll give you four cows for a horse, and then you'll have six times as many animals as I've got here."

    No doubt this was a very primitive way of bartering animals, but it is an interesting little puzzle to discover just how many animals Jakes, Hodge, and Durrant must have taken to the cattle market.

    Sources:

  • THE BEANFEAST PUZZLE

    A number of men went out together on a bean-feast. There were four parties invited—namely, `25` cobblers, `20` tailors, `18` hatters, and `12` glovers. They spent altogether £`6, 13`s. It was found that five cobblers spent as much as four tailors; that twelve tailors spent as much as nine hatters; and that six hatters spent as much as eight glovers. The puzzle is to find out how much each of the four parties spent. Sources:

  • A CHARITABLE BEQUEST

    A man left instructions to his executors to distribute once a year exactly fifty-five shillings among the poor of his parish; but they were only to continue the gift so long as they could make it in different ways, always giving eighteenpence each to a number of women and half a crown each to men. During how many years could the charity be administered? Of course, by "different ways" is meant a different number of men and women every time. Sources:

  • THE WIDOW'S LEGACY

    A gentleman who recently died left the sum of £`8,000` to be divided among his widow, five sons, and four daughters. He directed that every son should receive three times as much as a daughter, and that every daughter should have twice as much as their mother. What was the widow's share? Sources:

  • THE TWO AEROPLANES

    A man recently bought two aeroplanes, but afterwards found that they would not answer the purpose for which he wanted them. So he sold them for £`600` each, making a loss of `20` per cent, on one machine and a profit of `20` per cent, on the other. Did he make a profit on the whole transaction, or a loss? And how much? Sources:

  • 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?
    Sources:

  • 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: