An author received $0.80 in royalties for each of the first 100,000 co

Question

An author received $0.80 in royalties for each of the first 100,000 copies of her book sold, and $0.60 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold?

(A) 130,000
(B) 300,000
(C) 380,000
(D) 400,000
(E) 420,000

(A) 130,000
(B) 300,000
(C) 380,000
(D) 400,000
(E) 420,000

My Solution:

Lets assume total number of books sold = N

0.8 * 100,000 + (N-100,000) 6/10 = 260,000
(N-100,000) 6/10 = 260,000-80,000 = 180,000

Plugin answers:

I prefer to start with C, but B and D are easy to calculate. I pick D to start with.

(400,000 - 100, 000) 6/10= 300,000 * 6/10 = 180,000 Match with LHS to RHS.

Answer D is correct.

BrainLab · Accepted Answer

0.8*10^5+0.6*(x-10^5)=260000 
 10^5*0.2+0.6x=260000 
 x=400000 
Answer D

umasarath52 · Answer

Total royalties for first 100.000 books = .8*100,000= 80,000
Total royalties for the rest of the books = 260,000-80,000 = 180,000

Remaining books = 180,000/0.6 = 300,000

Total books = 300,000+100,000 = 400,000 Answer D

ScottTargetTestPrep · Answer

If we let n = the total number of copies sold, then (n - 100,000) is the number of additional copies (those in excess of 100,000) sold, and we can create the equation:

260,000 = 0.8 x 100,000 + 0.6(n - 100,000)

260,000 = 80,000 + 0.6n - 60,000

240,000 = 0.6n

400,000 = n

Answer: D

Abhishek009 · Answer

$260,000 = $0.80*100,000 + 0.60x

Or,  $260,000 = $80,000 + 0.60x

So,  x = 300,000

Hence, total no of copies sold is  300,000 + 100,000 = 400,000  , Answer must be (D)

MHIKER · Answer

Royalties from 100,000 copies =100,000*0.80=80,000

Left royalties = 160,000-80,000=180,000

Additional copies of book= \frac{180,000*100}{60}=300,000

Total copies of Book=100,000+300,000=400,000.

The answer is C

Pritishd · Answer

1. We can put up a nice equation to solve this one. Let  x  be the total copies of the books sold

2.  0.8 * 10^5 + 0.6 * (x - 10^5) = 2.6 * 10^5

3. We can replace  0.8  with  \frac{4}{5}  and  0.6  with  \frac{3}{5}  to make our calculations simpler

4.  \frac{4}{5} * 10^5 + \frac{3}{5} * (x - 10^5) = 2.6 * 10^5

5.  \frac{1}{5}  = 2.6 * 10^5

6.  3x + 10^5 = 13 * 10^5   OR   3x + 100000 = 1300000

7.  x = 4 * 10^5   OR   400000

Ans.  D

kapstone1996 · Answer

reduced 100,000 and $260,000 to hundreds, makes the arithmetic easier.

4/5(100) + 3/5 (x-100) = $260
80 + 3/5x-60 = $260
3/5x + 20 = $260
3/5x = $240
3x = 1200
x=400 or 400,000

Kinshook · Answer

Given: An author received $0.80 in royalties for each of the first 100,000 copies of her book sold, and $0.60 in royalties for each additional copy sold. 
Asked: If she received a total of $260,000 in royalties, how many copies of her book were sold?

Royalty for first 100,000 copies sold = $80,000
Royalty for remaining copies sold = $260,000 - $80,000 = $180,000
Additional copies sold = $180,000/$0.6 = 300,000

Number of copies sold = 100,000 + 300,000 = 400,000

IMO D

GMATWhizTeam · Answer

Royalty received by the author for the first 100,000 copies of her book = 0.80 * 100,000 = $80,000.
Since it is known that the author received a total of $260,000, it is easy to infer that more than 100,000 copies of the book was sold.

Let the additional copies sold be x. For each additional copy sold, royalty earned = $0.60
Therefore, total royalty earned on ‘x’ copies = 0.60 * x

The total royalty of $260,000 received by the author can be split into two components: $80,000 on the first 100,000 copies and $180,000 on the remaining x copies.

Therefore, 0.60 * x = 180,000

Solving for x, we have x = 300,000.

Total number of copies sold = 100,000 + x = 100,000 + 300,000 = 400,000
 The correct answer option is D.

Note that answer option B is a trap if you are not careful to understand that you are finding the total number of copies that were sold and NOT the copies over and above 100,000.

ThatDudeKnows · Answer

Whenever the instinct is to set up Algebra, I look to see if PITA (Plugging In The Answers) makes sense. In this case, it does.

Among B, C, and D, which looks easiest to work with? Either B or D. Let's try B.

If we sold 300,000 copies, we'd get 0.8 for each of the first 100.000 (so 80,000) and 0.6 for each of the other 200,000 (so 120,000). That adds up to 200,000, but we were looking for 260,000. B is wrong. Do we need something smaller or larger? Larger, so A is wrong. We are down to C, D, and E. D looks easy to work with, so let's try that.

If we sold 400,000 copies, we'd get 0.8 for each of the first 100.000 (so 80,000) and 0.6 for each of the other 300,000 (so 180,000). That adds up to 260,000, which is what we wanted. Done.

Answer choice D.

Bonus: Let's say D had been wrong. We would STILL have been done. If we needed something smaller than D, C would be the only option remaining. If we needed something larger than D, E would be the only option remaining. When using PITA, I frequently see people say to start with C. I actually like testing B and D whenever those answer choices have manageable numbers. They tell you everything you need to know. There are occasional questions where you might try C, it doesn't work, and then you have a hard time figuring out whether you want a larger number or a smaller one, so you might end up having to try one larger, realize you went the wrong way, and then try one smaller. If you do B first and it's wrong, you only have to try D. If you got farther away, you'd know it was A. If you need something between B and D, you'd know it was C. If you got closer but not all the way there, you'd know it was E.

ThatDudeKnowsPITA

Paras96 · Answer

Total royalties = royalties for the first 100,000 copies + royalties for additional copies

260,000=0.8*100,000 + 0.6*x
=> x=180,000/0.6
=> x=300,000

Total books sold = 100,000 + x = 100,000 + 300,000 = 400,000

Hence D

sujoykrdatta · Answer

Royalty from the first 100,000 copies = $100,000 * 0.8 = $80,000
Total royalty = $260,000
Remaining royalty = $260,000 - $80,000 = $180,000
Royalty for each additional copy = $0.60
=> Number of additional copies = 180000/0.6 = 300,000

Total copies = 100,000 + 300,000 = 400,000

Answer D

KevoK · Answer

For questions involving big numbers like this, I prefer trimming the number, and then add them back by the end:
So, now instead of the author recieving $0.8 for each of the 100,000 copy, she will recieve $0.8 for   1   copy sold. And 0.6 for each additional copy, which we will be  (n-1)  copies, where n is the total copies sold. The total royalties recieved will be 2.6$, we will have the formula:

0.8 + (n-1)*0.6 = 2.6

0.6n = 2.4

n = 4

now multiply back the 100,000 we have taken away, and we will have our answer

D 400,000

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