Hi,

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Here are the solutions:

The width of a rectangular screen on a portable DVD player is 5 cm less than the length. The area is 126. Find the length and the width.

Let L represent the length of the screen, and let W represent the width.

Since the width is 5 cm less than the length, we can write W = L - 5

The area is equal to the product of the length and the width, and is equal to 126 (square cm, I assume). This gives the following equation:

L * W = 126

Substituting for W gives:

L * (L - 5) = 126

Multiplying the terms on the left side gives:

L² - 5L = 126

Subtracting 126 from both sides gives:

L² - 5L - 126 = 0

This can be factored as:

(L + 9)(L - 14) = 0

Using the Principle of Zero Factors gives the two solutions:

L = -9 and L = 14

Since a negative length makes no sense in the context of the problem, the negative result is discarded.

The length is 14 cm.

The width is then 5 cm less than the length, or 14 - 5 = 9 cm

Solution:

Length = 14 cm

Width = 9 cm


A student opens a mathematics book to two facing pages. The product of the page numbers is 1980. Find the page numbers.

Let X represent the first page number.

The next page in the book is numbered X + 1.

The product of the two page numbers is X(X + 1), and is equal to 1980. This gives the equation:

X(X + 1) = 1980

Multiplying the terms on the left side gives:

X² + X = 1980

Subtracting 1980 from both sides gives:

X² + X - 1980 = 0

This can be factored as:

(X - 44)(X + 45) = 0

Using the Principle of Zero Factors, the solutions are:

X = 44 and X = -45

Again, the negative result is discarded.

The first page number is XXXXX

The second page number is XXXXX + 1 = 44 + 1 = 45


Solution:

First page number: 44

Second page number: 45


Note that in both problems, you could solve the quadratic equations using the Quadratic Formula instead of factoring. The results would be the same using either method.

Please feel free to ask if you have questions about either of these solutions.

Thanks,

Ryan