Draw Venn diagram with large outer circle (for park, A) enclosing 3 interlocking circles for hiking (H), camping (C) and picnicking (P). There are eight zones (Z1 to Z8) created by the circles and overlaps:
- Only camping (15)
- Only hiking (20)
- Only picnicking (35)
- Overlap C and H less Z7 (140)
- Overlap C and P less Z7 (125)
- Overlap H and P less Z7
- Overlap C, H and P
- A outside all 3 circles.
Write the numbers in their relevant zones.
H=Z2+Z4+Z6+Z7=210; Z1+...+Z8=300; C=Z1+Z4+Z5+Z7=185.
We can start plugging in actual numbers:
C=Z1+Z4+Z5+Z7 and Z4+Z7=140, so 185=C=15+140+125-Z7=280-Z7, so Z7=280-185=95.
Z5+Z7=125 and P=Z3+Z5+Z7+Z6=35+125+Z6=160+Z6; H=210=Z2+Z4+Z7+Z6, so Z6=210-20-140 and Z6=50 and therefore P=210. From Z7=95, Z5=125-95=30; Z4=140-95=45.
300=15+20+35+140+125+50+Z7+Z8=385-Z7+Z8 so Z8=Z7-85=95-85=10.
Since Z8=10 (no features), 300-10=290 parks have at least one feature.
Z7 is the zone where all three features overlap, so 95 parks have all three features.