Barstucks is making a new coffee blend. The company bought 50lbs. of Kona beans at $34.95 per lb. and plans to mix these beans with Columbian beans that sell for $7.99 per lb. wholesale. If Barstucks wants its cost of the blend to be $11.95 per lb., how many lbs. of Columbian beans should they buy?
C=number of pounds of Colombian required
then
50*34.95+C*7.99=(50+C)*11.95
Solve for C.
To find out how many pounds of Colombian beans Barstucks should buy, we can use a weighted average formula.
Let's assume the number of pounds of Colombian beans to be bought is 'x'.
The total cost of the Kona beans is 50 lbs. * $34.95 per lb. = $1747.50
The total cost of the Colombian beans is x lbs. * $7.99 per lb.
The total cost of the blend is the sum of the costs of the Kona and Colombian beans. Since the cost per pound of the blend is $11.95, we can set up the following equation:
($1747.50 + x lbs. * $7.99 per lb.) / (50 lbs. + x lbs.) = $11.95 per lb.
To solve this equation, we multiply both sides by (50 lbs. + x lbs.):
$1747.50 + x * $7.99 = $11.95 * (50 lbs. + x lbs.)
Expanding both sides of the equation:
$1747.50 + $7.99x = $597.50 + $11.95x
Rearranging the terms to isolate 'x', we get:
$11.95x - $7.99x = $1747.50 - $597.50
Simplifying:
$3.96x = $1150
Now, we can solve for 'x' by dividing both sides of the equation by $3.96:
x = $1150 / $3.96
x ≈ 290.40 lbs.
Therefore, Barstucks should buy approximately 290.40 pounds of Colombian beans.