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A writer is paid $1.50 per book in royalties for the first 50,000 copi

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A writer is paid $1.50 per book in royalties for the first 50,000 copi  [#permalink]

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New post 27 Sep 2018, 05:33
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A writer is paid $1.50 per book in royalties for the first 50,000 copies of his book sold, and $1.20 in royalties for each additional copy sold. If he received a total of $195,000 in royalties, how many copies of his book were sold?

(A) 100,000
(B) 120,000
(C) 140,000
(D) 150,000
(E) 200,000

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A writer is paid $1.50 per book in royalties for the first 50,000 copi  [#permalink]

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New post 27 Sep 2018, 07:17
1.5 = 3/2
1.2 = 6/5

Algebraically can be solved like this
195,000 = 50,000 * 3/2 + (x - 50,000) * 6/5

120,000 = (6/5)*x - 60,000

180,000 = (6/5)x

30,000 = (1/5)x = 150,000

Another way to solve this is backsolving

If we pick C 140,000 we take 50,000 copies out

We already have 75,000$ from the 50,000 copies but we need the remaining 120,000$

Remaining books royalities = 90,000 * (6/5) = 108,000 not enough.

So answer choice D

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Re: A writer is paid $1.50 per book in royalties for the first 50,000 copi  [#permalink]

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New post 28 Sep 2018, 00:28
For the first 50,000 copies -> he received $1.50*50,000= $75,000
For the remaining copies he received = $195,000- $75,000=$120,000

Number of copies he got $1.20= Total amount/royalty for each book = $120,000/$1.20=100,000 copies
100,000+50,000 = 150,000 copes = Answer D
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A writer is paid $1.50 per book in royalties for the first 50,000 copi  [#permalink]

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New post 28 Sep 2018, 06:28
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Bunuel wrote:
A writer is paid $1.50 per book in royalties for the first 50,000 copies of his book sold, and $1.20 in royalties for each additional copy sold. If he received a total of $195,000 in royalties, how many copies of his book were sold?

(A) 100,000
(B) 120,000
(C) 140,000
(D) 150,000
(E) 200,000

I suspect that solving this question is faster without algebra.
Trap answer is A (forgetting to add the first 50,000).
Using a running tally should help.

Running tally
• Batch 1, total royalties earned
First \(50,000\): total royalties at \($1.50\) each
\((50,000*$1.5)=(25,000*$3) = $75,000\)

(\(50,000\) sold)

• Batch 2, total royalties
\($(195,000-75,000)=$120,000\)

• Batch 2, # of copies?
Divide royalties by amount per copy
\(\frac{$120,000}{$1.2}=100,000\)

(+ \(100,000\) sold)

• Total # of copies sold
\((50,000 + 100,000) = 150,000\) copies

Answer D

Algebra - Given:
• Batch 1: first \(50,000, $1.50\) per copy
• Batch 2: after \(50,000\) copies: \($1.20\) per copy

Let \(x=\) # of copies sold at \($1.20\) ea

\(($1.5)(50,000)+($1.2)(x)=$195,000\)

\(($3)(25,000)+($1.2x)=$195,000\)

\($75,000+$1.2x=$195,000\)

\($1.2x=$120,000\)

\(x=\frac{$120,000}{$1.2}=\frac{$1,200,000}{$12}=100,000\)

Total # of copies sold: (Batch1) + (Batch2)
\((50,000+100,000)=150,000\)


Answer D
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Re: A writer is paid $1.50 per book in royalties for the first 50,000 copi  [#permalink]

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New post 28 Sep 2018, 12:54
1
Bunuel wrote:
A writer is paid $1.50 per book in royalties for the first 50,000 copies of his book sold, and $1.20 in royalties for each additional copy sold. If he received a total of $195,000 in royalties, how many copies of his book were sold?

(A) 100,000
(B) 120,000
(C) 140,000
(D) 150,000
(E) 200,000



\(195 = 1.5 *50 + 1.2(x-50)\)

\(195 = 75+1.2x-60\)

\(195 = 15+1.2x\)

\(180 = 1.2x\)

\(x = 150\)

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Re: A writer is paid $1.50 per book in royalties for the first 50,000 copi &nbs [#permalink] 28 Sep 2018, 12:54
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