A grocer buys lettuce for $2.60 a crate. Of the lettuce she buys, 10% spoils and cannot be sold. If she charges $0.20 for each head she sells, and makes a profit of $0.05 for each head she buys, how many heads of lettuce are in a crate? (Hint: profit = income - cost.)

Question

b87lar · Answer

Let n denote the number of lettuce heads in a crate. Then it is that $$0.9n*$0.02-$2.6=n*$0.05$$$$n(0.9*$0.05-$0.02)=$2.6$$$$n=$2.6/$0.025=104$$

anonymous · Answer

However, the n of your profit would also be based on the spoil rate...

I got: 

$0.05*n*0.9 = $0.20*n*0.9 - $2.60
$0.045*n - $0.18*n = - $2.60
-$0.135*n = -$2.60
n = -$2.60/-0.135
n = 19.259 OR 20 heads of lettuce per crate*

b87lar · Answer

Oh. Thanks for questioning my result. I noticed a few issues with my as well as your calculation. 
First mine: I made a mistake with $0.02 - this should be $0.2 all the way through. Secondly, the middle row is incorrectly manipulated. So the last row is incorrect. My corrections (starting from second row, first rows stays but with $0.2):$$0.9 n $0.2-$2.6=n$0.05$$$$n(0.9$0.2-$0.05)=$2.6$$$$n=$2.6/0.13=20$$
Second yours (I believe has this issue): you've added the spoil factor to both the sale price and the profit. But the original problem says: "she charges $0.20 for each head she *sells*, and makes a profit of $0.05 for each head she *buys*" (she buys 100% and sells only 90%). Agree?