Equations and Formulae Short Problems: Age 14-16

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Equations and Formulae: Age 14-16.

We have put together a selection of these short problems as printable worksheets:

Printable worksheet: Age 14-16 ⭐   Printable worksheets: Age 14-16 ⭐⭐   Printable worksheet solutions


  • Small pepper seedlings in orange pots.
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    Weighing the Baby

    Age
    14 to 16
    Challenge level

    Weighing the baby at the clinic was a problem. Can you work out the weight of the baby from the information given?

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    Adjacent Additions

    Age
    14 to 16
    Challenge level

    In a 7-digit numerical code, each group of four consecutive digits adds to 16, and each group of five consecutive digits adds to 19. What is the sum of all 7 digits?

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    In the Hundreds

    Age
    14 to 16
    Challenge level

    For how many positive values of $n$ are both $\frac n2$ and $2n$ three-digit whole numbers?

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    I Love Musical Stars

    Age
    14 to 16
    Challenge level

    Each row and column has the total given. What is the value of the heart symbol?

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    Table Total

    Age
    14 to 16
    Challenge level

    Can you find the sum of all of the numbers in the table?

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    Symmetric Reasoning

    Age
    14 to 16
    Challenge level

    Can you sum up the solutions to this equation?

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    Pure Algebra

    Age
    14 to 16
    Challenge level

    Can you work out the product of $a$ and $b$ from the information in the question?

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    Bat and Ball

    Age
    14 to 16
    Challenge level

    Can you work out how much this bat costs?

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    Terminology

    Age
    14 to 16
    Challenge level

    Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

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    Day of the Triffids

    Age
    14 to 16
    Challenge level

    Jasmine buys three different types of plant. How many triffids did she buy?

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    Fractions of Fractions

    Age
    14 to 16
    Challenge level

    If you know that a fraction of X is the same as a different fraction of Y, can you work out X/Y?

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    Table Height

    Age
    14 to 16
    Challenge level

    A table has blocks of wood placed on and next to it. Can you work out how tall it is?

  • Small pepper seedlings in orange pots.
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    Big Fish

    Age
    14 to 16
    Challenge level

    Granny has taken up deep-sea fishing! Last week, she caught a fish so big that she had to cut it into three pieces in order to weigh it...

  • Small pepper seedlings in orange pots.
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    Simultaneous Multiplying

    Age
    14 to 16
    Challenge level

    If $a \times b=2$, $b \times c=24$, $c \times a=3$ and $a$, $b$ and $c$ are positive, what is the value of $a+b+c$?

  • Small pepper seedlings in orange pots.
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    Monetary Difference

    Age
    14 to 16
    Challenge level

    Al, Bertie, Chris and Di have sums of money totalling £150... What is the difference between the amount Al and Di have?

  • Small pepper seedlings in orange pots.
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    Three Fruits

    Age
    14 to 16
    Challenge level

    Quince, quonce and quance are three types of fruit. Can you work out the order of heaviness of the fruits?

  • Small pepper seedlings in orange pots.
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    Weighing Scales

    Age
    14 to 16
    Challenge level

    Can you work out how many spheres will balance a single pyramid?

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    Average Surroundings

    Age
    14 to 16
    Challenge level

    Can you work out Ali's age based on the diagram?

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    Sum = Product = Quotient

    Age
    14 to 16
    Challenge level

    Can you find a pair of numbers such that their sum, product and quotient are all equal? Are there any other pairs?

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    Reciprocal Values

    Age
    14 to 16
    Challenge level

    Manipulate one algebraic fraction to solve another.

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    Near 10

    Age
    14 to 16
    Challenge level

    10 must remain within easy reach...

  • Small pepper seedlings in orange pots.
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    Packing Boxes

    Age
    14 to 16
    Challenge level

    Look at the times that Harry, Christine and Betty take to pack boxes when working in pairs, to find how fast Christine can pack boxes by herself.

  • Small pepper seedlings in orange pots.
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    Alien Currency

    Age
    14 to 16
    Challenge level

    The planet Zog has both green and blue bank notes. Can you work out how many zogs two green and three blue bank notes are worth?

  • Small pepper seedlings in orange pots.
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    Algebraic Differences

    Age
    14 to 16
    Challenge level

    If $6x-y=21$ and $6y-x=14$, what is the value of $x-y$?

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    Well Read

    Age
    14 to 16
    Challenge level

    If you know how many books each boy, girl and teddy bear borrowed from the library, can you work out the number of girls?

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    Oldest and Youngest

    Age
    14 to 16
    Challenge level

    Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?

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    Tennis Training

    Age
    14 to 16
    Challenge level

    After tennis training, Andy, Roger and Maria collect up the balls. Can you work out how many Andy collects?

  • Small pepper seedlings in orange pots.
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    Relative Angles

    Age
    14 to 16
    Challenge level

    Can you work out the angles of a triangle from the relationships between them?

  • Small pepper seedlings in orange pots.
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    Square to a Rectangle

    Age
    14 to 16
    Challenge level

    Kevin has moved some tiles to change the shape of his patio from a square to a rectangle. What are the lengths of the sides of the rectangle?

  • Small pepper seedlings in orange pots.
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    Black and White Socks

    Age
    14 to 16
    Challenge level

    There are 20 black socks and some white socks in a drawer. Can you work out how many of the socks are white?

  • Small pepper seedlings in orange pots.
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    Thousands of x

    Age
    14 to 16
    Challenge level

    Can you solve this scary-looking equation?

  • Small pepper seedlings in orange pots.
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    Traffic Tunnel

    Age
    14 to 16
    Challenge level

    Will these vehicles fit through this tunnel?

  • Small pepper seedlings in orange pots.
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    Nested Square Roots

    Age
    14 to 16
    Challenge level

    Can you find the value of this expression, which contains infinitely nested square roots?

  • Small pepper seedlings in orange pots.
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    A Third of the Area

    Age
    14 to 16
    Challenge level

    The area of the small square is $\frac13$ of the area of the large square. What is $\frac xy$?

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