A group of children visited the Botanic Gardens one morning. The number of boys was $50 \%$ more than the number of girls. Later in the afternoon, $$12$$ boys and $$12$$ girls joined the group. The ratio of the number of boys to girls became $$19 : 14$$. Find the total number of children in the Botanic Gardens that afternoon.~\uline{~~~~~~~~~~}~     Ollie\textquotesingle s workings:  \uline{Before (morning)}  Boys $:$ Girls $:$ Difference  $2:1:1$  $10:5:5$  \uline{After (afternoon)}  Boys $:$ Girls $:$ Difference  $19:14:5$  The boys and girls increased by $9u$ each.  $9u=12$  Total $=19u+14u=33u=\frac{12}{9}\times33=44$  There were $44$ children.     Observe Ollie\textquotesingle s workings above and try to spot a mistake, if any. Write down your workings and solve the question. 
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