Skip over navigation
Cambridge University Faculty of Mathematics NRich logo
menu search
  • Teachers expand_more
    • Early years
    • Primary
    • Secondary
    • Post-16
    • Events
    • Professional development
  • Students expand_more
    • Primary
    • Secondary
    • Post-16
  • Parents expand_more
    • Early Years
    • Primary
    • Secondary
    • Post-16
  • Problem-Solving Schools
  • About NRICH expand_more
    • About us
    • Impact stories
    • Support us
    • Our funders
    • Contact us
  • search

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Developing positive attitudes
  • Cross-curricular contexts

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Grow up Fast

Age 11 to 14
ShortChallenge Level Yellow star
Secondary curriculum
  • Problem
  • Solutions

Answer: 59


Using the number of years that have passed
    Julie     Megan       Zoey    
  today     32     4     1  
  in $n$ years     32 + $n$     4 + $n$     1 + $n$  

32 + $n$ = 4 + $n$ + 1 + $n$
            = 5 + 2$n$
27 = $n$

In 27 years Julie will be 32 + 27 = 59


Using algebra and Julie's age
Julie's age is $J$

$32-4=28$ so Megan's age is $J-28$
$32-1=31$ so Zoey's age is $J-31$
$$\begin{align}(J-28)+(J-31)&=J\\
\Rightarrow 2J-59&=J\\
\Rightarrow J&=59\end{align}$$ So Julie will be $59$.


Using trial
  Julie     Megan      Zoey      M + Z    
  32     4     1      
  42     14     11     25     too small  
  52     24     21     45     too small
  62     34     31     65     too big  
  61     33     30     63     too big
  59     31     28     59     perfect  

Julie is 59


 

You can find more short problems, arranged by curriculum topic, in our short problems collection.

You may also like

Hallway Borders

What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?

Not a Polite Question

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

Linkage

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

  • Tech help
  • Accessibility Statement
  • Sign up to our newsletter
  • Twitter X logo

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

University of Cambridge logo NRICH logo