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Mars2501 [29]
2 years ago
10

Is it possible to arrange 152 books on a shelf so that the first shelf has 7 fewer books than the second shelf and 11 more than

the third shelf?
Mathematics
1 answer:
Zepler [3.9K]2 years ago
7 0

Using a system of equations, it is found that <u>since the solution of the system does not involve decimal numbers</u>, it is possible to arrange the books in this way.

For the system, we consider that:

  • x is the number of books on the first shelf.
  • y is the number of books on the second shelf.
  • z is the number of books on the third shelf.

In total, there are 152 books, hence:

x + y + z = 152

The first shelf has 7 fewer books than the second shelf, hence:

x = y - 7

Also, it has 11 more books than the third shelf, hence:

x = z + 11

Then:

y - 7 = z + 11

z = y - 18

Then, replacing in the first equation:

x + y + z = 152

y - 7 + y + y - 18 = 152

3y = 177

y = \frac{177}{3}

y = 59

The number of books in each shelf has to be countable, that is, cannot be decimal.

  • Then, <u>since the solution of the system does not involve decimal numbers</u>, it is possible to arrange the books in this way.

To learn more about system of equations, you can take a look at brainly.com/question/14183076

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Answer:

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Completing the square follows the principle of taking a x^{2} +bx+c and converting it into (x+ \frac{b}{2})^2+d where d is the 'correctional number' as I like to call it - i.e. the number that converts the expanded bracket into the +c, since the expanded bracket will give us a x^{2} +b.

In this case, 2/2=1 so we have the first part: (w+1)^2.
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