# Simultaneous Equations

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). Plymouth University workbook

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’

Since it’s Easter an updated version of the best Easter Eggs of all – from WolframAlpha.

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