1. **State the problem:** Find the sum of the place values of 7 and 8 in the number 78777. 2. **Identify the digits and their places:** The number is 78,777. 3. From left to right, the digits are: 7 (ten thousands), 8 (thousands), 7 (hundreds), 7 (tens), 7 (units). 4. **Calculate place value of 7 in the ten thousands place:** $$7 \times 10,000 = 70,000$$ 5. **Calculate place value of 8 in the thousands place:** $$8 \times 1,000 = 8,000$$ 6. **Sum the place values:** $$70,000 + 8,000 = 78,000$$ 7. **Final answer:** The sum of the place values of 7 and 8 in 78777 is 78000.