Question

How many pounds of coffee worth $1.50 per pound should be mixed with coffee worth $2.00 per

pound to obtain 3 pounds of a new blend worth $1.70 per pound?

Answer 1

1.8 pounds of coffee worth $ 1.50 per pound should be mixed with 1.2 pounds of coffee worth $ 2.00 per pound to obtain 3 pounds of a new blend worth $ 1.70 per pound

Solution:

Let "x" be the pounds of coffee worth $ 1.50 per pound

Then, (3 - x) be the pounds of coffee worth $ 2.00 per pound

So, "x" pounds of coffee worth $ 1.50 per pound should be mixed with (3 - x) pounds of coffee worth $ 2.00 per pound to obtain 3 pounds of a new blend worth $ 1.70 per pound

Therefore, a equation is framed as,

`1.50 * x + (3-x) * 2.00 = 3 * 1.70\\\\1.50x +2(3-x) = 5.1`

Solve the above equation for "x"

`1.50x +2(3-x) = 5.1\\\\1.50x + 6 - 2x = 5.1\\\\-0.5x = 5.1 - 6\\\\-0.5x=-0.9\\\\0.5x = 0.9\\\\x = 1.8`

Therefore, we need 1.8 pounds of coffee worth $ 1.50 per pound

Then, (3 - x) = 3 - 1.8 = 1.2 pounds of coffee worth $ 2.00 per pound