1. **State the problem:** We have a 100 gram metal alloy that is 40% silver. It is made by mixing two metal alloys: the first is 65% silver and the second is 25% silver. We need to find the mass of the first metal alloy. 2. **Define variables:** Let $x$ be the mass (in grams) of the first metal alloy (65% silver). Then the mass of the second metal alloy is $100 - x$ grams. 3. **Set up the equation for silver content:** The total silver in the mixture is 40% of 100 grams, which is 40 grams. The silver from the first alloy is $0.65x$ grams. The silver from the second alloy is $0.25(100 - x)$ grams. 4. **Write the equation:** $$0.65x + 0.25(100 - x) = 40$$ 5. **Simplify and solve:** $$0.65x + 25 - 0.25x = 40$$ $$0.40x + 25 = 40$$ $$0.40x = 15$$ $$x = \frac{15}{0.40} = 37.5$$ 6. **Answer:** The mass of the first metal alloy is **37.5 grams**.