Arecipe calls for mixed nuts with 50% peanuts. 1/2 pound of 15% peanuts has already been used. how many pounds of 75% peanuts needs to be added to obtain the 50% mix?

Now you have

(.15)0.5 lb peanuts     =     0.075 lb peanuts
0.5 lb  nuts                              0.5 lb nuts

for every pound of 75% mixed nuts you add, you get .75 lb peanuts, how many pounds, x, do you need to add to get the ratio 50 to 100?

0.075 lb peanuts + 0.75x lb peanuts       =       50   
0.5 lb nuts + x lb nuts                                      100

cross multiply

(0.075 + .75x) 100 = (0.5 + x) 50
7.5 + 75x = 25 + 50x
25x = 17.5
x = 0.7 lb of 75% peanuts