1. **State the problem:** Yoko's Coffee Shop makes a blend of two types of coffee: Type A costs 4.05 per pound, Type B costs 5.80 per pound. The total blend is 158 pounds and costs 797.40 in total. We need to find how many pounds of Type A coffee were used. 2. **Define variables:** Let $x$ be the pounds of Type A coffee. Then, the pounds of Type B coffee is $158 - x$. 3. **Set up the cost equation:** Total cost = (cost per pound of A) * (pounds of A) + (cost per pound of B) * (pounds of B) $$4.05x + 5.80(158 - x) = 797.40$$ 4. **Expand and simplify:** $$4.05x + 5.80 \times 158 - 5.80x = 797.40$$ Calculate $5.80 \times 158$: $$5.80 \times 158 = 916.40$$ So, $$4.05x + 916.40 - 5.80x = 797.40$$ 5. **Combine like terms:** $$4.05x - 5.80x + 916.40 = 797.40$$ $$-1.75x + 916.40 = 797.40$$ 6. **Isolate $x$:** Subtract 916.40 from both sides: $$-1.75x + 916.40 - 916.40 = 797.40 - 916.40$$ $$-1.75x = -119.00$$ 7. **Divide both sides by -1.75:** $$x = \frac{-119.00}{-1.75}$$ Show cancellation: $$x = \frac{\cancel{-119.00}}{\cancel{-1.75}} = 68$$ 8. **Interpretation:** Yoko used 68 pounds of Type A coffee. **Final answer:** $$\boxed{68}$$ pounds of Type A coffee.