Problem Solving

a certain used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times dealer's cost. last week the dealer sold a total of 120 books, each of which had cost the dealer $1. if the gross profit(sales revenue minus dealer's cost) on the sale of all of these books was $300, how many of the books sold were paperbacks?
a)40
b)60
c)75
d)90
e)100




the answer is not provided.


actually, does it have an answer?

let's say that the number of Paperbacks is X, hence the number of Hardbacks is 120 - X


REVENUE - COSTS = PROFIT


revenue from paperbacks = 3*1$*X
revenue from hardbacks = 4*1$*(120 - X)
total revenue = 3X + 4(120-X)
total costs= 120*1$

3X + 4(120-X) - 120 = 300
3x + 480 - 4x - 120 - 300 = 0
60 = x

answer is should be B[/b]

hakyology wrote:a certain used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times dealer's cost. last week the dealer sold a total of 120 books, each of which had cost the dealer $1. if the gross profit(sales revenue minus dealer's cost) on the sale of all of these books was $300, how many of the books sold were paperbacks?
a)40
b)60
c)75
d)90
e)100

Perfect question for backsolving!

We know that the profit on paperbacks is $2 ($3 - $1) and the profit on hardcovers is $3 ($4 - $1).

Using the Kaplan method for backsolving, we start with either (b) or (d). Let's choose (b) (for no particular reason).

If the dealer sold 60 paperbacks, then she also sold 60 hardcovers (total books is 120). So, profit is:

60(2) + 60(3) = 120 + 180 = 300... bingo! That's exactly what we wanted, so choose (b).

If (b) had given us too low a profit, then we'd want to decrease the number of paperbacks and would have automatically chosen (a). If (b) had given us too much profit, then we'd want to increase the number of paperbacks and tried (d) next.

If you start with either (b) or (d) and can figure out which direction to go if your first answer doesn't work, then you have a 40% chance to get it right with just 1 try and you're guaranteed to find the right answer on your 2nd try.

As an aside, we can make the algebra much simpler if we focus on profit right away, instead of revenue.

Letting p = the # of paperbacks and h = the # of hardcovers, we can set up the dual equations:

p + h = 120

and

2p + 3h = 300

and solve for p.