1. **State the problem:** We have two sauces being mixed: one is 5 ounces with 50% tangy mustard, and the other has an unknown amount $x$ ounces with 75% tangy mustard. The resulting mixture is $5 + x$ ounces with 70% tangy mustard. 2. **Formula and explanation:** The amount of tangy mustard in the mixture is the sum of the tangy mustard amounts from each sauce. We use the equation: $$\text{(amount of mustard in first sauce)} + \text{(amount of mustard in second sauce)} = \text{(amount of mustard in mixture)}$$ 3. **Set up the equation:** $$5 \times 0.50 + x \times 0.75 = (5 + x) \times 0.70$$ 4. **Simplify and solve:** $$2.5 + 0.75x = 3.5 + 0.70x$$ Subtract $0.70x$ from both sides: $$2.5 + 0.05x = 3.5$$ Subtract 2.5 from both sides: $$0.05x = 1.0$$ Divide both sides by 0.05: $$x = \frac{1.0}{0.05} = 20$$ 5. **Interpretation:** The chef must have used 20 ounces of the 75% tangy mustard sauce to get the final mixture with 70% tangy mustard. **Final answer:** $$\boxed{20}$$ ounces