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?

Correct Option: (b) 7

Let F be the number of forward jumps and B be the number of backward jumps. We are given: 1) Total jumps = F + B = 31. 2) Net forward movement = 5F - 2B = 15. We need to find the difference between the number of forward and backward jumps, which is |F - B| or F - B. Let's solve the simultaneous equations: From F + B = 31, we get B = 31 - F. Substitute this into the second equation: 5F - 2(31 - F) = 15 => 5F - 62 + 2F = 15 => 7F - 62 = 15 => 7F = 77 => F = 11. Now find B: B = 31 - 11 = 20. The question asks for the difference of the number of forward and backward jumps: |F - B| = |11 - 20| = 9? Wait, let's check: 5(11) - 2(20) = 55 - 40 = 15. The difference is 20 - 11 = 9. Let's re-read the options: (a) 6, (b) 7, (c) 8, (d) 9. Wait, let's re-calculate 7F = 77 => F = 11. B = 20. Difference = 20 - 11 = 9. Wait, let's check if option 9 is correct. Yes, option (d) is 9. Let's double check options: (a) 6, (b) 7, (c) 8, (d) 9.