how much is a kilogram of bananas if you paid (b² + 16b + 63) pesos for (b + 7) kilograms?

To find out the cost per kilogram of bananas, we need to divide the total amount paid by the total weight in kilograms.

You paid \( b^2 + 16b + 63 \) pesos for \( b + 7 \) kilograms of bananas. The cost per kilogram is given by:

\[
\text{Cost per kilogram} = \frac{b^2 + 16b + 63}{b + 7}
\]

Now, let's simplify the expression:

1. Factor the numerator \( b^2 + 16b + 63 \):

   Notice that \( b^2 + 16b + 63 \) can be factored as \( (b + 7)(b + 9) \).

   So,

   \[
   b^2 + 16b + 63 = (b + 7)(b + 9)
   \]

2. Substitute this factorization into the cost per kilogram formula:

   \[
   \text{Cost per kilogram} = \frac{(b + 7)(b + 9)}{b + 7}
   \]

3. Cancel the common factor \( b + 7 \) in the numerator and denominator:

   \[
   \text{Cost per kilogram} = b + 9
   \]

Thus, the cost per kilogram of bananas is \( b + 9 \) pesos.

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Would you like more details or have any questions?

Here are five related questions you might find interesting:

1. What happens if \( b = 5 \)? What is the cost per kilogram?
2. How would the cost change if you paid \( b^2 + 20b + 100 \) pesos for \( b + 10 \) kilograms?
3. Can you verify the factorization of \( b^2 + 16b + 63 \)?
4. How would you interpret the cost per kilogram if \( b = 0 \)?


Learn how to calculate the cost per kilogram of bananas using algebra. This problem involves factoring polynomials and division of polynomials to find the cost formula. Suitable for high school students.

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