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

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

\($260,000 = $0.80*100,000 + 0.60x\)

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)

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

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. \(\frac{1}{5}[4 * 10^5 + 3x - 3 * 10^5] = 2.6 * 10^5\)

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

7. \(x = 4 * 10^5\) OR \(400000\)

Ans. D

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

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

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.

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

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

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