Brazilian coffee costs $7.00/lb, and Columbian coffee costs $9.00/lb. How many pounds of Columbian coffee can be added to 30lb of Brazilian coffee to make a blend that costs no more than $7.50/lb?

From 1 to 10 pounds of Colombian coffee can be added to make a blend that costs no more than US$ 7.50 per pound. If we add 11 or more, the blend will cost more than US$ 7.50 per pound.

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Price of the Brazilian coffee = US$ 7 per pound

Price of the Colombian coffee = US$ 9 per pound

Amount of Brazilian coffee to make a blend = 30 pounds

2. How many pounds of Colombian coffee can be added to 30 pounds of Brazilian coffee to make a blend that costs no more than $7.50/lb?

Amount of Colombian coffee to make a blend = x pounds

We will use the following linear equation to solve for x, this way:

(30 * 7 + x * 9) / (30 + x) = 7.50

(210 + 9x) / (30 + x) = 7.50

210 + 9x = 7.50 (30 + x) (Multiplying by 30 + x at both sides)

210 + 9x = 225 + 7.5x

9x - 7.5x = 225 - 210 (Like terms)

1.5x = 15

x = 15/1.5 = 10

From 1 to 10 pounds of Colombian coffee can be added to make a blend that costs no more than US$ 7.50 per pound. If we add 11 or more, the blend will cost more than US$ 7.50 per pound.