1. **State the problem:** Tomas’ Mexican Restaurant wants to mix extra hot salsa (\$12 per pound) and medium salsa (\$8 per pound) to create 40 pounds of spicy salsa selling at \$9 per pound. We need to find how many pounds of each salsa to mix so that the revenue of the new blend equals the sum of revenues of the old blends. 2. **Define variables:** Let $x$ = pounds of extra hot salsa, $y$ = pounds of medium salsa. 3. **Set up equations:** - Total weight: $$x + y = 40$$ - Revenue equality: Revenue from extra hot + medium = Revenue from spicy blend Revenue from extra hot: $12x$ Revenue from medium: $8y$ Revenue from spicy blend: $9 \times 40 = 360$ So, $$12x + 8y = 360$$ 4. **Solve the system:** From the first equation, $$y = 40 - x$$ Substitute into the revenue equation: $$12x + 8(40 - x) = 360$$ $$12x + 320 - 8x = 360$$ $$4x + 320 = 360$$ $$4x = 40$$ $$x = 10$$ Then, $$y = 40 - 10 = 30$$ 5. **Interpretation:** Mix 10 pounds of extra hot salsa and 30 pounds of medium salsa. 6. **Check revenue:** $$12 \times 10 + 8 \times 30 = 120 + 240 = 360$$ matches the spicy salsa revenue. **Final answer:** $(10,30)$