There are 27 boys on the playground.
Step-by-step explanation:
No. of Pre-K children = 34
No. of kindergarten children = 29
Total no of children = 29+34 = 63
Ratio of boys to girls = 3:4
Total ratio = 3+4 = 7
Therefore,
boys proportion = 
Total number of boys = 

There are 27 boys on the playground.
Keywords: Proportion, division.
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Let's treat that one as a 4 by 8 rectangle with a 2 by 4 right triangle chopped out of the corner.
A = 4×8 - (1/2)×2×4 = 32 - 4 = 28
Answer: 28