Three tour groups have 10, 15 and 25 members with mean ages 30 years, 24 years and $x$ years. The mean age of all 50 tourists is 27 years. Find $x$.

The total age of all 50 tourists is $50\times 27=1350$ years. The first two groups contribute $10\times 30+15\times 24=300+360=660$ years, so the third group contributes 1350 − 660 = 690 years over 25 members, giving $x=690÷25=27.6$ years. Solving $(30+24+x)/3=27$ would wrongly give $x=27$, treating the three groups as equal in size when the third is the largest.