Chapter 4.1, Problem 68E

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Chapter
Section

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

# Publishing (from the GMAT) There were 36,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold, nine times as many paperback copies as hardback copies were sold. If a total of 441,000 copies of the novel were sold in all, how many paperback copies were sold?

To determine

To calculate: The number of paperback copies sold, if the total number of 36,000 hard-back copies of a particular novel sold before the paperback version was issued. The total number of 441,000 copies of that novel were sold in all.

Explanation

Given Information:

The total number of 36,000 hard-back copies of a particular novel sold before the paperback version was issued. The total number of 441,000 copies of that novel were sold in all.

Formula used:

Elimination method:

Step 1: Consider the linear equations in two variables.

Step 2: The equations are multiplied with suitable non-zero numbers to convert the coefficients to equals of opposite signs.

Step 3: The equations are combined to eliminate one variable, and the value of the other variable is calculated.

Step 4: Substitute the value of the calculated variable into one of the equations and calculate the value of the other variable.

Calculation:

Consider the problem,

Let x be the number of paperback copies sold and y be the number of hardback copies sold after the paperback version was issued.

From the time, the first paperback copy sold until the last copy of that novel was sold, nine times as many paperback copies as hardback copies were sold.

Thus,

x=9y

Rewrite x=9y in standard form,

xā9y=0

Also, the total number of 36,000 hard-back copies of a particular novel sold before the paperback version was issued. The total number of 441,000 copies of that novel were sold in all.

Therefore, the total copies of the novel after the paperback version issued,

441,000ā36,000=405,000

Here, if x paperback copies were sold and y hardback copies were sold after the paperback version was issued, then the total number of copies sold was x+y. But the total copies of the novel after the paperback version issued was 405,000.

Thus,

x+y=405,000

Consider the equations,

xā9y=0 ā¦ā¦ (1)

x+y=405,000 ā¦ā¦ (2)

Multiply the equation (2) by ā1,

ā1ā(

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