a company bought 50lb of kona beans at $34.95 per lb. and plans to mix these with colombian beans at $7.99 per lb. wholesale. If they want the blend to be $11.95 per lb, how many lbs of colombian beans should they buy?
i believe the answer is 290.4 pounds? if someone would like to back me up on this answer thatd be great
To find out how many pounds of Colombian beans the company should buy, we can use the weighted average formula.
Let's assume that the company needs to buy 'x' pounds of Colombian beans.
The total cost of Kona beans is 50 × $34.95 = $1747.50.
The total cost of Colombian beans is 'x' × $7.99 = $7.99x.
The total cost of the blend is 50 × $11.95 = $597.50.
Since the blend is a combination of Kona and Colombian beans, the total cost of the blend is the sum of the costs of the Kona and Colombian beans. Therefore, we can set up the equation:
$1747.50 + $7.99x = $597.50
Simplifying the equation, we get:
$7.99x = $597.50 - $1747.50
$7.99x = -$1150
x = -$1150 / $7.99
x ≈ 144.06 pounds
Since we cannot buy a fractional amount of beans, the company should buy approximately 144 pounds of Colombian beans to achieve the desired blend.