Question

How much Active Mix should she add in order to have a trail mix containing 30% dried fruit?
lbs

Answer 1

I don’t have enough information to give a numeric answer. I need:
- how many pounds of trail mix she already has (A),
- the percent of dried fruit in that current mix (p%),
- the percent of dried fruit in the Active Mix (q%).

If you want the general formula, let x = pounds of Active Mix to add. Then the equation for 30% dried fruit is
(A·p + x·q) / (A + x) = 30%.

Solving for x gives
x = A·(30 − p) / (q − 30).

Notes:
- q must not equal 30 (otherwise either you already are at 30% or it’s impossible to change the percentage by adding that mix).
- The sign of the numerator and denominator must match so x > 0 (e.g., if p < 30 you need q > 30; if p > 30 you need q < 30).

Give me A, p, and q and I’ll compute the pounds to add.