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

  • THE BICYCLE THIEF

    Here is a little tangle that is perpetually cropping up in various guises. A cyclist bought a bicycle for £`15` and gave in payment a cheque for £`25`. The seller went to a neighbouring shopkeeper and got him to change the cheque for him, and the cyclist, having received his £`10` change, mounted the machine and disappeared. The cheque proved to be valueless, and the salesman was requested by his neighbour to refund the amount he had received. To do this, he was compelled to borrow the £`25` from a friend, as the cyclist forgot to leave his address, and could not be found. Now, as the bicycle cost the salesman £`11`, how much money did he lose altogether?

    Topics:
    Algebra -> Word Problems
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  • THE COSTERMONGER'S PUZZLE

    "How much did yer pay for them oranges, Bill?"

    "I ain't a-goin' to tell yer, Jim. But I beat the old cove down fourpence a hundred."

    "What good did that do yer?"

    "Well, it meant five more oranges on every ten shillin's-worth."

    Now, what price did Bill actually pay for the oranges? There is only one rate that will fit in with his statements.

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  • MAMMA'S AGE

    Tommy: "How old are you, mamma?"

    Mamma: "Let me think, Tommy. Well, our three ages add up to exactly seventy years."

    Tommy: "That's a lot, isn't it? And how old are you, papa?"

    Papa: "Just six times as old as you, my son."

    Tommy: "Shall I ever be half as old as you, papa?"

    Papa: "Yes, Tommy; and when that happens our three ages will add up to exactly twice as much as to-day."

    Tommy: "And supposing I was born before you, papa; and supposing mamma had forgot all about it, and hadn't been at home when I came; and supposing——"

    Mamma: "Supposing, Tommy, we talk about bed. Come along, darling. You'll have a headache."

    Now, if Tommy had been some years older he might have calculated the exact ages of his parents from the information they had given him. Can you find out the exact age of mamma?

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  • THEIR AGES

    "My husband's age," remarked a lady the other day, "is represented by the figures of my own age reversed. He is my senior, and the difference between our ages is one-eleventh of their sum." Sources:

  • THE FAMILY AGES

    When the Smileys recently received a visit from the favourite uncle, the fond parents had all the five children brought into his presence. First came Billie and little Gertrude, and the uncle was informed that the boy was exactly twice as old as the girl. Then Henrietta arrived, and it was pointed out that the combined ages of herself and Gertrude equalled twice the age of Billie. Then Charlie came running in, and somebody remarked that now the combined ages of the two boys were exactly twice the combined ages of the two girls. The uncle was expressing his astonishment at these coincidences when Janet came in. "Ah! uncle," she exclaimed, "you have actually arrived on my twenty-first birthday!" To this Mr. Smiley added the final staggerer: "Yes, and now the combined ages of the three girls are exactly equal to twice the combined ages of the two boys." Can you give the age of each child? Sources:

  • MRS. TIMPKINS'S AGE

    Edwin: "Do you know, when the Timpkinses married eighteen years ago Timpkins was three times as old as his wife, and to-day he is just twice as old as she?"

    Angelina: "Then how old was Mrs. Timpkins on the wedding day?"

    Can you answer Angelina's question?

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  • A CENSUS PUZZLE

    Mr. and Mrs. Jorkins have fifteen children, all born at intervals of one year and a half. Miss Ada Jorkins, the eldest, had an objection to state her age to the census man, but she admitted that she was just seven times older than little Johnnie, the youngest of all. What was Ada's age? Do not too hastily assume that you have solved this little poser. You may find that you have made a bad blunder! Sources:

  • MOTHER AND DAUGHTER

    "Mother, I wish you would give me a bicycle," said a girl of twelve the other day.

    "I do not think you are old enough yet, my dear," was the reply. "When I am only three times as old as you are you shall have one."

    Now, the mother's age is forty-five years. When may the young lady expect to receive her present?

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  • MARY AND MARMADUKE

    Marmaduke: "Do you know, dear, that in seven years' time our combined ages will be sixty-three years?"

    Mary: "Is that really so? And yet it is a fact that when you were my present age you were twice as old as I was then. I worked it out last night."

    Now, what are the ages of Mary and Marmaduke?

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  • ROVER'S AGE

    "Now, then, Tommy, how old is Rover?" Mildred's young man asked her brother.

    "Well, five years ago," was the youngster's reply, "sister was four times older than the dog, but now she is only three times as old."

    Can you tell Rover's age?

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