The owner of the Koffee Shop pours the remainder of her old house blend, which is 45% Colombian beans, into a 40-pound bin, and fills it up with her new house blend, which is 20% Colombian beans. Let h stand for the number of pounds of the old house blend. Write algebraic expressions to answer the questions below.
To answer the questions, we need to express the quantities in terms of h, which represents the number of pounds of the old house blend.
1. What is the total amount of the new house blend in the bin?
Since the old house blend is poured first into the bin, it contributes h pounds. The remaining amount in the bin is filled with the new house blend, which is (40 - h) pounds.
2. What is the amount of Colombian beans in the old house blend?
If the old house blend is 45% Colombian beans, then the amount of Colombian beans in the old house blend is 0.45h pounds.
3. What is the amount of Colombian beans in the new house blend?
If the new house blend is 20% Colombian beans, then the amount of Colombian beans in the new house blend is 0.20(40 - h) pounds.
Note: Since you mentioned "algebraic expressions," I provided expressions using algebraic notation.