Answer:
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.
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.