The weight of the fat in each of the components of the mixture must add up to the weight of the fat in the total mix, so: 

. Just solve for  to get your answer.

30 lbs of 15% has 30 * .15 = 4.5 lbs of pure fat.

we want "total fat" divided by "pure beef" to be .10 (10%) by adding beef that is 7% fat:

(.15*30 + .07*x)/(30+x) = .10

(4.5 + .07x) = (3 + .1x)

1.5 = .03x

x = 50

so we need to add 50 lbs of 7% fat in order to obtain 10% fat... in the end, we have 80 lbs of beef