Substitution (Simultaneous Equation) Puzzles

[TheLovelyBoots]

I found this puzzle on the NLCS 11+ sample paper. Can you suggest where I might find more? (I couldn't copy/paste, sigh)

heart triangle smileyface triangle = 99
smileyface triangle triangle heart = 99
heart smileyface heart smileyface = 154
triangle heart smileyface triangle = 99
= = = =
142 99 ? 99

It sorta helps to assume that the numbers are all being added. Is that right? Then the problem makes sense. Comparing two pairs of different rows and columns give
smiley = triangle +12;
heart = triangle + 43;
Then writing any one of the 99 rows all in terms of triangles gives triangle = 11. The rest follows, e.g. smiley = 23 etc.

That's right. My question is where I might find a worksheet of such puzzles? I can find only very few one-offs.

www.tes.co.uk/teaching-resource/Simultaneous-Equations-Puzzles-3006908/

This is an excel spreadsheet which will let you generate your own puzzles of this type

You'll need to create a TES account first though.

My point was rather to check first that you meant addition was being applied to the symbols. Once you know that just make up some other combinations of 3 weird symbols, give them each a value and put them in a grid in such a way that you have 3 independent combinations to add up that are shown as row or column totals. If you have less than 3 independent sums exposed there could be more than one answer so make sure that is right. You really can just make these up. You could explore working with 2 symbols or perhaps 4 to give kids something to think about.