Set up the variables fine, cows = x, chickens = 2x, spiders = 4x.
Translate the word problem into algebraic equations by assigning variables to each animal type, then use the given relationships to express all variables in terms of one variable. Solve the resulting equation for the base variable, then compute the number of spiders.
Pro tip: After solving, verify your answer by plugging the numbers back into the original problem to ensure all conditions are satisfied. This catches arithmetic errors and demonstrates thoroughness.
Let S = number of spiders, C = number of chickens, and W = number of cows (use W to avoid confusion with C for chickens).
Translate the given relationships into equations: C = 2W (chickens are twice cows) and S = 2C (spiders are twice chickens).
Set up the total legs equation: 8S + 2C + 4W = 520.
Substitute S and C in terms of W into the leg equation, simplify, and solve for W. Then find S = 4W.
Check that the total legs match 520 and that all relationships hold, then state the number of spiders.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.