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The problem states that a cereal box manufacturer changes the size of the box, and two expressions represent the amount of cereal in the larger box and the smaller boxes. These expressions are:

- For the larger box: \( 12 + 7.5n \)
- For the smaller boxes: \( 8 + 7.7n \)

where \( n \) represents the number of smaller boxes.

We are tasked with finding how many smaller boxes have the same amount of cereal as the larger box. To do that, we need to equate the two expressions and solve for \( n \).

### Equation setup:

\[
12 + 7.5n = 8 + 7.7n
\]

Now, we can solve for \( n \).

### Solving the equation:

1. Subtract \( 7.5n \) from both sides:

\[
12 = 8 + 0.2n
\]

2. Subtract 8 from both sides:

\[
4 = 0.2n
\]

3. Divide both sides by 0.2:

\[
n = \frac{4}{0.2} = 20
\]

Thus, the larger box has as much cereal as **20 smaller boxes**.

Would you like a more detailed explanation or have any questions?

Here are 5 related questions for further practice:
1. What would happen if the cereal box manufacturer increased the larger box's size by 2 units in the expression?
2. How would the result change if the smaller box’s content was reduced by 1 unit?
3. Can you write a general formula for solving this type of problem with different constants?
4. What if the expression for the larger box was quadratic, like \(12 + 7.5n^2\)? How would you solve it?
5. How many smaller boxes would be needed if the expression was \(12 + 8n\) for the larger box?

**Tip**: Always isolate the variable step by step when solving equations.

A cereal box manufacturer changes the size of the box to increase the amount of cereal it contains. The expressions 12 + 7.5n and 8 + 7.7n, where n is the number of smaller boxes, are both representative of the amount of cereal that the new larger box contains. How many smaller boxes equal the same amount of cereal in the larger box?

Learn how to solve a linear equation comparing the amount of cereal in different sized boxes. This problem explores algebraic concepts by solving the equation 12 + 7.5n = 8 + 7.7n to find how many smaller boxes equal the same amount as the larger box. Suitable for Grades 6-8.

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