Expert: Ahmed Salami - 6/15/2004

Question
Hiiiiiiiii

please I need you help to solve this problem thank you so much



A coffee manufacturer wants to markets a new blend of coffee that sells for $3.90 per pound by mixing two coffee that sell for $2.75 and $5 per pound, respectively. What amount of each coffee should be blended to obtain the desired mixture?

Hint; Assume that the total weight of the desired blend is 100pound.


thank you so much  

Answer
Hi jacira,
If tha amount of the $2.75 coffee is x pounds, the amount of the $5 coffee should be (100 - x)pounds since the amount should add up to 100 pounds.
The total money to be realised from the sale of the new blend would be $3.90(100) = $390
Therefore,
390 = 2.75x + 5(100 - x)
390 = 2.75x + 500 - 5x
390 = 500 - 2.25x
2.25x = 500 - 390 = 110
x = 110/2.25 = 48.8888888....
Just as a little note.
Now, if this amount can't be accurately measured
It is better to take it as 49pounds for then there would be no loss.
As a check,
2.75(49) + 5(100 - 49) = 2.75(49) + 5(51)
= 134.75 + 255 = $389.75
This is the amount it would cost you.
If you had taken it as 48pounds, you would run at a little loss.
I hope this helps.
Regards.