**An Easter puzzle from MathisFun** – as an excuse for solving simultaneous equations. We could of course use algebra. Using the notation, h, q and t for the egg Horace wants, the egg with the small square pattern and the egg with the stripey pattern respectively.

We have:

h + 2q =550 (1)

h + q +t =600 (2)

—-2q +t =500 (3)

Subtracting equation (3) from equation (2) gives

h−q=100 (4)

(1)−(4) gives 3q=450 so q=150 and h must be 250 ($2.50).

We could check our solution on WolframAlpha of course:

Did you know that you can easily invert matrices and solve simultaneous equations using Excel?

Select the image or this link for the Excel file. **Excel simultaneous equations**

To enter the MINVERSE function in the example above, select cells C7:E9, enter the MINVERSE function as shown then press CTRL + SHIFT + ENTER; similarly to enter the MMULT function in this example, select cells H7:H9, enter the MMULT function as shown and then press CTRL + SHIFT + ENTER. (Using formulae like these demonstrates a neat Excel technique, to learn more see **MrExcel on Array Formulae**).

For notes / examples / tutorials on Simultaneous Equations try the **mathcentre resources **or **this workbook from Plymouth University**. For more on solving three equations in three unknowns for older students see **Simultaneous Linear Equations **from** AJ Hobson’s ‘Just the Maths’ **

If you want some more puzzles, **MathisFun has plenty more**, or try some of the **puzzles here.**