The coffee counter charges $8 per pound for kenyan french roast and $12 per pound for sumatran coffee. how much of each type should be used to make a 26 pound blend that sells for $10 per pound ?

Use k pounds of Kenyan coffee and s pounds of Sumatran.  Then k + s = 26lb.

Cost of Kenyan coffee is ($8/lb)k, and cost of Sumat. coff. is ($12/lb)s 

($8/lb)k + ($12/lb)s must = ($10/lb)(26 lb)

Then 8k + 12s = 260, and k=26-s.

Substituting,    8(26-s) + 12s = 260.    208 - 8s + 12s = 260.  This boils down to 4s = 52, and so s = 13 (lb).  Then k = 26-13 = 13 lb.

Check:  ($8/lb)(13 lb) + ($12/lb)(13 lb) must add up to ($10/lb)(26 lb.  Do they?