If a dictionary is sold at its marked price, then the percentage profit is 30%. If the dictionary is sold at a 20% discount on its marked price, then the profit is $5. Find the cost of the dictionary.

Question

anonymous · Answer

what was the ans to prev q you posted?

anonymous · Answer

$120

anonymous · Answer

so i was right..yay  :)

anonymous · Answer

this one is more tricky though

anonymous · Answer

@dlearner and yet i cannot get the answer

anonymous · Answer

the previous question

anonymous · Answer

did you see my post?

anonymous · Answer

yes, but i still don't understand

anonymous · Answer

wait a min

anonymous · Answer

i'll post in that question

anonymous · Answer

ok thankd

anonymous · Answer

s*

anonymous · Answer

let discuss this question

anonymous · Answer

Three variables $m, c, d$ for marked price, cost, and discount price respectively.

If a dictionary is sold at its marked price, then the percentage profit is 30%.
>Profit is 30% of marked price
$$
m - c = 0.30 m
$$

anonymous · Answer

If the dictionary is sold at a 20% discount on its marked price
$$
d = 0.20 m
$$
then the profit is $5. $$
d - c = 5
$$

anonymous · Answer

3 equations, three variables... shouldn't be too hard.

anonymous · Answer

Whoops, one of my equations is wrong

anonymous · Answer

If the dictionary is sold at a 20% discount on its marked price
$$
d = m-0.20m
$$

anonymous · Answer

Summary: $$
m-c = 0.3m \
d-c = 5 \
d = m - 0.20m = 0.80m
$$

anonymous · Answer

i'm getting $50 for the thing

anonymous · Answer

Let $\bf x$ denote the price of the dictionary. We know that the when the dictionary is sold at $\bf x$ dollars, the seller gets 30% profit, i.e from the money he gets for the dictionary, 30% of that money is profit hence the profit is $\bf 0.3x$. Now we also know that the profit when the price is decreased by 20% is $5, i.e. when the price is $\bf 0.8x$, the profit is $\bf $5$. But we know that from a price $\bf x$, he makes $\bf 0.3x$ which means that the book cost the seller about $\bf 0.7x$. But when it's sold at 20% off, the book is getting the seller about $\bf 0.8x$ dollars which is $\bf 0.1x $ more than the price he bought the book at and this 0.1x profit is $5. Hence:$$\bf 0.1x=5 \implies x = $50$$

@kryton1212

anonymous · Answer

how about this: see that the markoff comes directly off the profit. 30% of the initial price is profit. Taking 20% off as a discount leaves us with 70% value and 10% profit. We know this 10% profit is $5. From there we can multiply to find the answer.

anonymous · Answer

but there're only four choices which are :
A. $104
B. $105
C. $125
D. $270

anonymous · Answer

wat lol then i misinterpreted the question?

anonymous · Answer

@Peter14 That's what I did too but apparently it's not right 0,o

anonymous · Answer

nah, assume the question is wrong

anonymous · Answer

nani

anonymous · Answer

what was that?

anonymous · Answer

nani = what?!
"nani" is Japanese...

anonymous · Answer

it means "what?!"
that's not the point...

anonymous · Answer

so now the question is, how are you going to communicate to the teacher that the actual answer is what you have and not one of the choices...

anonymous · Answer

how about if the profit is $50 instead of $5 ?

anonymous · Answer

lol?

anonymous · Answer

Then you get $500..

anonymous · Answer

i mean if the question is being like this:
.......If the dictionary is sold at a 20% discount on its marked price, then the profit is $50.

anonymous · Answer

what?! $500 @@...

anonymous · Answer

yes, he's right

anonymous · Answer

ohh, but there're only that four answers for us to choose............
the question is wrong ?

anonymous · Answer

yes, as I said earlier

anonymous · Answer

oh
my
gosh

anonymous · Answer

this question is public exam question..

anonymous · Answer

there might be something we're overlooking...

anonymous · Answer

O.o

anonymous · Answer

$5.....

anonymous · Answer

lol @Peter14

anonymous · Answer

the answer of this question is $125

anonymous · Answer

that makes no sense at all.

anonymous · Answer

ummmmmmmmmmmmmmmmmmmm

anonymous · Answer

@kryton1212 u sure the question here is the way it is on the paper?

anonymous · Answer

yes, i am sure

anonymous · Answer

can we discuss this question after you answer my next question?

anonymous · Answer

@genius12

hero · Answer

s = selling price
c = cost
p = profit

p = s - c

$$\frac{s - c}{c} = .30$$
$$.8s - c = 5$$

s - c = .30c
.8s - c  = 5

s = 1.30c
c = .8s - 5

c = .8(1.30c) - 5
c = 1.04c - 5

5 = 1.04c - c
5 = .04c

5/.04 = c
125 = c

The original cost of dictionary was $125

hero · Answer

You're welcome