If three identical cylinders weigh as much as five identical spheres, and three of these spheres weigh as much as twelve identical cubes, then how many cylinders weigh as much as sixty cubes?

3 Cylinders = 5 Spheres (1)

3 Spheres = 12 Cubes (2)

Multiply (2) by 5 on each side

60 Cubes = 15 Spheres (3)

Multiply (1) by 3 on each side

9 Cylinders = 15 Spheres (4)

So (3) and (4) imply that

9 Cylinders = 60 Cubes

3x=5y

3y=12z

15y=60z

9x=15y

9 cylinders