1. **State the problem:** We need to find the mean (average) price of the binoculars given the prices: 129, 55, 99, 54, 74, 59, 112, 38. 2. **Formula for mean:** The mean is calculated by summing all the values and then dividing by the number of values. $$\text{Mean} = \frac{\text{Sum of all prices}}{\text{Number of prices}}$$ 3. **Calculate the sum:** $$129 + 55 + 99 + 54 + 74 + 59 + 112 + 38 = 620$$ 4. **Count the number of prices:** There are 8 prices. 5. **Calculate the mean:** $$\text{Mean} = \frac{620}{8}$$ 6. **Simplify the fraction:** $$\frac{\cancel{620}}{\cancel{8}} = 77$$ 7. **Interpretation:** The mean price of the binoculars is 77 dollars. **Final answer:** $$\boxed{77}$$