I have tried to answer this question for a couple of hours now!

Question

A grocery store is reevaluating the retail price of their oranges. They have a contract where they can purchase oranges for $0.52 per pound. However, this includes high quality oranges (about 40% of shipments), low quality oranges (55%), and occasionally rotten fruit (5%). Suppose they sell 80% of all high quality oranges at $1.99 per pound, 65% of all low quality oranges at $1.49 per pound (they offer a sale), and they cannot sell any of the rotten fruit.

What percent of the oranges that they buy do they actually sell? (Round your percent answer to two decimal places.)

Answer 1

Let total purchased = t

High quality=h=40% of total

or h=.4*t

Low quality=l=55% of total

or l=.55*t

Rotten=r=5% of total

or r=.05*t

Let total sold=s

High quality sales = 80% of purchased high quality oranges

or h(sold)=.8*h(purchased)=.8*(.4*t)

Low  quality sales = 65% of purchased low quality oranges

or l(sold)=.65*l(purchased)=.65*(.55*t)

No rotten oranges are sold, so total sales is the sum of low and high quality oranges, or

Sales = l(sold) + h(sold)

=.8*(.4*t)+.65*(.55*t)

=.32*t+.36*t

=.68*t, or

68% of the total purchased.

Answer 2

They sell 80% of the 40% high quality. That is 32% of the shipment.

They sell 65% of the 55% low quality. That is 37.75% of the shipment

They sell what percent in all?