A toy T jumps forward or backward. In each forward jump, it moves 5' forward whereas in each backward jump, it moves 2' backward. If in 31 jumps, T moves exactly 15' forward, then what is the difference of the number of forward and backward jumps?

Let f = forward jumps and b = backward jumps. Then f + b = 31 and 5f – 2b = 15. From the first: b = 31 – f. Substituting: 5f – 2(31 – f) = 15, so 5f – 62 + 2f = 15, hence 7f = 77, giving f = 11 and b = 20. Difference = b – f = 9, or |f – b| = 9. Wait, re-check: 7f = 77 gives f=11, b=20. Difference = 20 – 11 = 9. But verify: 5(11) – 2(20) = 55 – 40 = 15 ✓. So difference = 9. Hmm, the answer would be (d) 9. Let me reconsider whether it's forward – backward or absolute difference. The question says 'difference of the number of forward and backward jumps' = |11 – 20| = 9. Answer is 9, option (d).