1. **State the problem:** Carter has a total of 50 pigs and cows. The number of cows is ten less than three times the number of pigs. We need to find how many pigs Carter has. 2. **Define variables:** Let $p$ be the number of pigs and $c$ be the number of cows. 3. **Write the equations based on the problem:** - Total animals: $$p + c = 50$$ - Relationship between cows and pigs: $$c = 3p - 10$$ 4. **Substitute the second equation into the first:** $$p + (3p - 10) = 50$$ 5. **Simplify the equation:** $$p + 3p - 10 = 50$$ $$4p - 10 = 50$$ 6. **Add 10 to both sides:** $$4p - 10 + 10 = 50 + 10$$ $$4p = 60$$ 7. **Divide both sides by 4:** $$\frac{4p}{\cancel{4}} = \frac{60}{\cancel{4}}$$ $$p = 15$$ 8. **Conclusion:** Carter has **15 pigs**.