9 years ago Spiderman's age was twice Superman's age. 9 years hence,…

A word problem that describes one unknown's relationship to another unknown at two different times translates into a system of two linear equations in two unknowns. Solve the system (by substitution or elimination) to find each unknown's present value, then convert the required value to the requested number base.

1. Let Spiderman's present age be x years and Superman's present age be y years.

2. 9 years ago, Spiderman's age was twice Superman's age: x - 9 = 2(y - 9), which simplifies to x - 2y = -9 ... equation (1)

3. 9 years hence, Spiderman's age will be 4/3 times Superman's age: x + 9 = (4/3)(y + 9). Multiplying both sides by 3: 3x + 27 = 4y + 36, which simplifies to 3x - 4y = 9 ... equation (2)

4. From equation (1), x = 2y - 9. Substituting into equation (2): 3(2y - 9) - 4y = 9, so 6y - 27 - 4y = 9, so 2y = 36, so y = 18.

5. Then x = 2(18) - 9 = 27. So Spiderman's present age is 27 years.

6. Convert 27 to binary by repeated division by 2, reading the remainders bottom to top: 27 = 11011 in binary (16 + 8 + 2 + 1 = 27).

Check: 9 years ago, Spiderman was 27 - 9 = 18 and Superman was 18 - 9 = 9; 18 equals 2 times 9. 9 years hence, Spiderman will be 27 + 9 = 36 and Superman will be 18 + 9 = 27; 36 equals 4/3 times 27. Both conditions hold, confirming the binary value 11011.