How many pounds of each type of nut should be used in the mixture?

Question

To make a special mix, the owner of a fruit and a nut stand wants to combine cashews that sell for $7 per lb with walnuts that sell for $5.50 per lb to obtain 35 lb of a mixture that sells for $6.50 per lb. 

Answer 1

Let x = lbs of cashews

Then, 35 -x = lbs of walnuts

(x)($7) + (35 -x)($5.5) = (35)($6.5)

7x + 192.5 - 5.5x = 227.5

1.5x = 35

x = 23.3 lbs of cashews

35 - x = 35 - 23.3 = 11.7 lbs of walnuts

 

Done by alligation:

HAVE..........NEED.........WANT...

$7.....................................1........

....................6.50........................

$5.50.............................0.5........

Total parts = 1.5 = 35 lbs

1 part = 35/1.5 = 23.3 lbs of the $7 cashews

0.5 parts = 17.5/1.5 = 11.7 lbs of $5.50 walnuts