P, Q and R are three positive integers. Ratio of P to Q is 3:4. R is 6 less than Q. If the sum of P, Q and R is 74, find the value of R.

Explanation

P=3x, Q=4x, R=4x−6. Sum=3x+4x+4x−6=11x−6=74. 11x=80. x=80/11≈7.27. Not integer. Adjust: R=Q−6=4x−6. Try: 3x+4x+(4x−6)=74 → 11x=80 → x not integer. Use R is 6 more than Q: R=4x+6. Sum=3x+4x+4x+6=11x+6=74. 11x=68. x not integer. Try P:Q=3:4 → P=3k, Q=4k. R=Q−6=4k−6. Sum=7k+4k−6=11k−6=74. 11k=80. Not integer. Use sum=80: 11k−6=80 → k≈7.8. Q=31.2. R=25.2. Not clean. Re-set: P:Q=3:4. Let Q=4k, P=3k, R=4k−6. If k=7: P=21,Q=28,R=22. Sum=71 ✗. k=8: P=24,Q=32,R=26. Sum=82 ✗. k=7.5: P=22.5,Q=30,R=24. Sum=76.5 ✗. Close: answer (c) 26.