Just a note. There is a subtle difference in using LCM units and 100u (an easy and quick fix especially for question with %) and any other units or algebra. End results will be the same so it is up to individual preference, as long as the user’s mind is clear on what the unknown denotes.
However, based on my experience, if I use LCM units and get “u” as not a whole number, then I know immediately somewhere I have been careless and will stop and do a quick check. For 100u or some other “u”, it is possible to get a fraction or decimal answer for “u” and additional check is needed to put the “u” value back into the working to ensure accuracy. For this question, there is 135u and 85u involved and putting 5.2 into 135u and 85u gives whole number which makes sense for no. of girls and boys.
You can even don’t think about LCM units or 100u and just put a “G” for no. of girls and still can get the correct answer. Just that double checking is more necessary. See below where I picked from BigDevil’s workings (credit to BigDevil), but using “G” for no. of girls. (and this will look more like my old school algebra method.)
Boys -> G + 940
Girls -> G
Boys down to (100% – 15%) = 85% -> 0.85 x (G + 940) = 0.85G + 799
Girls up by 35% -> 1.35 x G = 1.35G
Total -> 1943
0.85G + 799 + 1.35G = 1943
2.2G = 1144
G = 520 [additional check 0.85G=442 is ok, 1.35G=702 is ok]
Boys in July -> 0.85G + 799 = (0.85 x 520) + 799 = 1241
Hope this puts your mind at ease from worrying about choosing the “correct” units. But I do suggest you try LCM units sometimes to get more practice and a good grasp of what LCM units represent and how they help in solving some unique questions. Do also have a play with 10u like you have asked earlier. You will still get same results. See another example here if you like.
I also see some workings in your picture where child has written 15% = 3/20, 35% = 7/20. For these two fractions, the LCM units is 20u. Increase or decrease from 20u can easily be converted to increase or decrease by 3u or 7u, that is why the ease of use for LCM units. Same goes for 100u and % changes.