# Equations and Formulae Stage 3 - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Equations and Formulae - Stage 3.

Printable worksheets containing selections of these problems are available here:

 Stage 3 ★ Sheet 1 Solutions Stage 3 ★★ Sheet 1 Solutions

### Fifty Coins

##### KS 3 Short Challenge Level:

Weekly Problem 50 - 2014
Cheryl finds a bag of coins. Can you work out how many more 5p coins than 2p coins are in the bag?

### Tennis Training

##### KS 3 Short Challenge Level:

Weekly Problem 40 - 2017
After tennis training, Andy, Roger and Maria collect up the balls. Can you work out how many Andy collects?

### Seven Dwarfs

##### KS 3 Short Challenge Level:

Weekly Problem 13 - 2010
The Seven Dwarfs have seven different birthdays. How old can they be?

### Between a Square and a Cube

##### KS 3 Short Challenge Level:

Weekly Problem 51 - 2011
The equation $x^2+2=y^3$ looks nearly quadratic. What integer solutions can you find?

### Helen's Family

##### KS 3 Short Challenge Level:

Weekly Problem 42 - 2017
Helen has twice as many sisters as brothers. Her brother Tim has three times as many sisters as brothers. How many children are there in the family?

### Equal Means

##### KS 3 Short Challenge Level:

Weekly Problem 36 - 2017
What value of x makes the mean of the first three numbers in this list equal to the mean of the other four?

### Five-to

##### KS 3 Short Challenge Level:

Weekly Problem 22 - 2015
The number 2005 is the sum of a sequence of five consecutive positive integers. What is the smallest of these integers?

##### KS 3 Short Challenge Level:

Weekly Problem 49 - 2017
Each interior angle in a quadrilateral (apart from the smallest) is twice the previous one. What is the size of the smallest interior angle?

### Packing Boxes

##### KS 3 Short Challenge Level:

Weekly Problem 28 - 2011
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.

### Turnips

##### KS 3 Short Challenge Level:

Weekly Problem 37 - 2012
Baldrick could buy 6 parsnips and 7 turnips, or 8 parsnips and 4 turnips. How many parsnips could he buy?

### Oldest and Youngest

##### KS 3 Short Challenge Level:

Weekly Problem 11 - 2017
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?

### Debt Recovery

##### KS 3 Short Challenge Level:

Weekly Problem 7 - 2009
Tony and Tina can't work out which of them owes what to the other. Can you?

### Shape Sums

##### KS 3 Short Challenge Level:

Weekly Problem 22 - 2016
Given some relationships amongst these shapes, how many triangles equal one diamond?

### Corner Cut

##### KS 3 Short Challenge Level:

Weekly Problem 23 - 2017
Three small equilateral triangles of the same size are cut from the corners of a larger equilateral triangle. What is the side length of the small triangles?

### Average Surroundings

##### KS 3 Short Challenge Level:

Weekly Problem 15 - 2009
Can you work out Ali's age based on the diagram?

### Cube Pile

##### KS 3 Short Challenge Level:

Weekly Problem 29 - 2017
Rick has five cubes. Each one is 2cm taller than the previous one. The largest cube is the same height as a tower built of the two smallest cubes. How high would a tower of all five cubes be?

### Currency Exchange

##### KS 3 Short Challenge Level:

Weekly Problem 48 - 2009
Dan and Ann have 9 and 8 coins respectively. What is the smallest number of coins they must swap so they end up with equal amounts of money.

### Partial Magic

##### KS 3 Short Challenge Level:

Weekly Problem 41 - 2011
This magic square has only been partially completed. Can you still solve it...

### Symbol

##### KS 3 Short Challenge Level:

Weekly Problem 2 - 2011
Using the new operator $\oplus$, can you solve this equation?

### Fractions of Fractions

##### KS 3 Short Challenge Level:

Weekly Problem 44 - 2013
If you know that a fraction of X is the same as a different fraction of Y, can you work out X/Y?

### Monetary Difference

##### KS 3 Short Challenge Level:

Weekly Problem 50 - 2007
Al, Bertie, Chris and Di have sums of money totalling £150... What is the difference between the amount Al and Di have?

### Alien Currency

##### KS 3 Short Challenge Level:

Weekly Problem 22 - 2014
The planet Zog has both green and blue banknotes. Can you work out how many zogs two green banknotes and three blue banknotes are worth?

### To Run or Not to Run?

##### KS 3 Short Challenge Level:

Weekly Problem 38 - 2012
If an athlete takes 10 minutes longer to walk, run and cycle three miles than he does to cycle all three miles, how long does it take him?

### Star Sum

##### KS 3 Short Challenge Level:

Weekly Problem 40 - 2011
You may have seen magic squares before, but can you work out the missing numbers on this magic star?

### Traffic Jam

##### KS 3 Short Challenge Level:

Weekly Problem 1 - 2017
Yesterday evening, Emily's journey home took 25% longer than usual. By what percentage was her average speed reduced compared to normal?

### Magic 7

##### KS 3 Short Challenge Level:

Weekly Problem 36 - 2015
Can you complete this magic square with the numbers from 7 to 15?

### Granny's Age

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 10 - 2015
Granny is four times as old as I am. Five years ago she was five times as old as I was. What is the sum of our ages?

### Square and Cube

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 24 - 2014
The square of a positive number is twice as big as the cube of that number. What is the number?

### Triangular Algebra

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 26 - 2017
The angles in the triangle are shown in the diagram in terms of x and y. If x and y are positive integers, what is the value of x+y?

### Bookshop

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 3 - 2017
Books cost £3.40 and magazines cost £1.60. If Clara spends £23 on books and Magazines, how many of each does she buy?

### Hillwalking

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 40 - 2016
Andrew walks along a flat path, then up and down a hill, then back along the path. Is it possible to work out how far he has walked?

### Algebraic Differences

##### KS 4 Short Challenge Level:

Weekly Problem 42 - 2014
If $6x−y=21$ and $6y−x=14$, what is the value of $x−y$?