Jackson has x chocolate bars. He has 436 more milk chocolate bars than dark chocolate bars.

(a)  How many milk chocolate bars does Jackson have? Express your answer in terms of x. 

(b)  Jackson consumes 16% more dark chocolate bars than milk chocolate bars. After eating, there are 472 more milk chocolate bars than dark chocolate bars remaining. Form an equation to determine the number of milk chocolate bars left. 

(c)  What is the total number of chocolate bars remaining? Express your answer in terms of x.

Let's break down the problem step by step.

### (a) How many milk chocolate bars does Jackson have? Express your answer in terms of \( x \).

Let:
- \( d \) represent the number of dark chocolate bars.
- \( m \) represent the number of milk chocolate bars.

According to the problem, Jackson has 436 more milk chocolate bars than dark chocolate bars, so we can express this as:

\[
m = d + 436
\]

Since \( x \) represents the total number of chocolate bars, we have:

\[
x = m + d
\]

Substituting the expression for \( m \) from the first equation:

\[
x = (d + 436) + d
\]

Simplifying this:

\[
x = 2d + 436
\]

Thus, the number of milk chocolate bars Jackson has is:

\[
m = d + 436
\]

We can express \( d \) in terms of \( x \):

\[
d = \frac{x - 436}{2}
\]

Substitute \( d \) back into \( m = d + 436 \):

\[
m = \frac{x - 436}{2} + 436
\]

### (b) Jackson consumes 16% more dark chocolate bars than milk chocolate bars. After eating, there are 472 more milk chocolate bars than dark chocolate bars remaining.

Let:
- \( m' \) represent the number of milk chocolate bars remaining after eating.
- \( d' \) represent the number of dark chocolate bars remaining after eating.

Given:
- Jackson consumes 16% more dark chocolate bars than milk chocolate bars.
- After eating, there are 472 more milk chocolate bars than dark chocolate bars remaining.

The number of chocolate bars consumed:
- Dark chocolate bars consumed: \( d - d' \)
- Milk chocolate bars consumed: \( m - m' \)

Since he consumes 16% more dark chocolate bars:

\[
d - d' = 1.16 \times (m - m')
\]

The remaining number of chocolate bars gives us:

\[
m' = d' + 472
\]

Substituting \( d' + 472 \) for \( m' \) into the first equation:

\[
d - d' = 1.16 \times \left( m - (d' + 472) \right)
\]

Simplify:

\[
d - d' = 1.16 \times (m - d' - 472)
\]

This equation can be used to determine the number of milk chocolate bars left, \( m' \).

### (c) What is the total number of chocolate bars remaining? Express your answer in terms of \( x \).

The total number of chocolate bars remaining is \( m' + d' \).

Using the relationship \( m' = d' + 472 \):

\[
\text{Total remaining} = m' + d' = (d' + 472) + d' = 2d' + 472
\]

We already have \( d' = \frac{x - 436}{2} - \frac{d - d'}{2} \), but simplifying requires knowing the consumed amounts, which is embedded in the previous equations. However, for now, we could express this in a generalized form using \( d' \).

\[
\text{Total remaining} = 2d' + 472
\]

Would you like to proceed with solving for \( d' \) and \( m' \) or get more details on any part? 

### Relative Questions

1. How do you find the number of dark chocolate bars from the total number \( x \)?
2. What happens to the total chocolate bars if Jackson eats more than 16% extra dark chocolate bars?
3. How would you adjust the equations if Jackson ate more milk chocolate bars than dark?
4. Can the total number of chocolate bars ever be less than 472? Why?
5. How does the equation change if there were 472 fewer milk chocolate bars instead?

### Tip

When solving equations involving percentages, always ensure you convert the percentage into a decimal form before multiplying it with other terms.

Explore how to solve problems involving chocolate bars using algebraic equations and percentage calculations. This problem includes determining quantities of milk and dark chocolate bars based on given conditions and constraints. Suitable for high school students (Grades 9-12).

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