1. **State the problem:** There are 36 cookies in total. The number of peanut butter cookies equals the sum of all other types. There are 4 more sugar cookies than chocolate chip cookies. There are 16 fewer oatmeal cookies than peanut butter cookies. We need to find how many cookies there are of each type. 2. **Define variables:** Let: - $p$ = number of peanut butter cookies - $s$ = number of sugar cookies - $c$ = number of chocolate chip cookies - $o$ = number of oatmeal cookies 3. **Write equations from the problem:** - Total cookies: $$p + s + c + o = 36$$ - Peanut butter equals all others combined: $$p = s + c + o$$ - Sugar cookies are 4 more than chocolate chip: $$s = c + 4$$ - Oatmeal cookies are 16 fewer than peanut butter: $$o = p - 16$$ 4. **Substitute $p = s + c + o$ into total cookies equation:** $$p + s + c + o = 36$$ Replace $p$: $$(s + c + o) + s + c + o = 36$$ Simplify: $$2s + 2c + 2o = 36$$ Divide both sides by 2: $$\cancel{2}s + \cancel{2}c + \cancel{2}o = \cancel{2}18$$ $$s + c + o = 18$$ 5. **Recall from step 3 that $p = s + c + o$, so:** $$p = 18$$ 6. **Use $o = p - 16$ to find $o$:** $$o = 18 - 16 = 2$$ 7. **Use $s = c + 4$ and substitute $s$ and $o$ into $s + c + o = 18$:** $$(c + 4) + c + 2 = 18$$ Simplify: $$2c + 6 = 18$$ Subtract 6: $$2c = 12$$ Divide both sides by 2: $$\cancel{2}c = \cancel{2}6$$ $$c = 6$$ 8. **Find $s$ using $s = c + 4$:** $$s = 6 + 4 = 10$$ 9. **Summary of results:** - Peanut butter cookies: $p = 18$ - Sugar cookies: $s = 10$ - Chocolate chip cookies: $c = 6$ - Oatmeal cookies: $o = 2$ 10. **Check total:** $$18 + 10 + 6 + 2 = 36$$ Correct. **Final answer:** There are 18 peanut butter cookies, 10 sugar cookies, 6 chocolate chip cookies, and 2 oatmeal cookies.