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Answer :
To solve the problem, let's work through it step-by-step:
1. Understanding the Problem:
Albert flips open his mathematics textbook and sees two facing pages. The product of the page numbers is given as 156. We need to identify the correct equation that represents this relationship.
2. Identify the Facing Page Numbers:
When you open a book, the left page has a number, say [tex]\( x \)[/tex], and the right page will have the next number, [tex]\( x + 1 \)[/tex]. This is because page numbers increase sequentially in a book.
3. Set Up the Equation:
Given that the product of the page numbers is 156, we can express this situation mathematically as:
[tex]\[
x \times (x + 1) = 156
\][/tex]
4. Evaluate the Provided Options:
- Option 1: [tex]\( x + (x + 1) = 156 \)[/tex] involves addition, not multiplication, so it's incorrect.
- Option 2: [tex]\( (x + 1) + (x + 2) = 156 \)[/tex] also involves addition, which doesn't match our problem statement.
- Option 3: [tex]\( (x + 1)(x + 3) = 156 \)[/tex] assumes the numbers are separated by 2, which is incorrect for consecutive pages.
- Option 4: [tex]\( x(x + 1) = 156 \)[/tex] correctly represents the product of the two consecutive facing pages.
5. Conclusion:
The correct equation that can be used to find the page numbers Albert is looking at is option 4: [tex]\( x(x + 1) = 156 \)[/tex].
Therefore, the answer is option 4.
1. Understanding the Problem:
Albert flips open his mathematics textbook and sees two facing pages. The product of the page numbers is given as 156. We need to identify the correct equation that represents this relationship.
2. Identify the Facing Page Numbers:
When you open a book, the left page has a number, say [tex]\( x \)[/tex], and the right page will have the next number, [tex]\( x + 1 \)[/tex]. This is because page numbers increase sequentially in a book.
3. Set Up the Equation:
Given that the product of the page numbers is 156, we can express this situation mathematically as:
[tex]\[
x \times (x + 1) = 156
\][/tex]
4. Evaluate the Provided Options:
- Option 1: [tex]\( x + (x + 1) = 156 \)[/tex] involves addition, not multiplication, so it's incorrect.
- Option 2: [tex]\( (x + 1) + (x + 2) = 156 \)[/tex] also involves addition, which doesn't match our problem statement.
- Option 3: [tex]\( (x + 1)(x + 3) = 156 \)[/tex] assumes the numbers are separated by 2, which is incorrect for consecutive pages.
- Option 4: [tex]\( x(x + 1) = 156 \)[/tex] correctly represents the product of the two consecutive facing pages.
5. Conclusion:
The correct equation that can be used to find the page numbers Albert is looking at is option 4: [tex]\( x(x + 1) = 156 \)[/tex].
Therefore, the answer is option 4.
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