A baker has some flour and sugar. At first there were 5 times as much flour than sugar. After 3.2 kg of flour and 3.2 kg of sugar were used, the difference in the amount of flour and sugar left was 28.6kg. How much flour was there at first?

Let's define the amount of sugar at first as \( x \) kg. Since the baker originally had 5 times as much flour as sugar, the amount of flour at first was \( 5x \) kg.

### Step-by-step process:
1. **Before usage:**
   - Amount of sugar = \( x \) kg
   - Amount of flour = \( 5x \) kg

2. **After using 3.2 kg of both flour and sugar:**
   - Amount of sugar left = \( x - 3.2 \) kg
   - Amount of flour left = \( 5x - 3.2 \) kg

3. **Difference between the amount of flour and sugar left:**
   - According to the problem, the difference between the amount of flour and sugar left is 28.6 kg:
   \[
   (5x - 3.2) - (x - 3.2) = 28.6
   \]

4. **Simplify the equation:**
   \[
   5x - 3.2 - x + 3.2 = 28.6
   \]
   \[
   4x = 28.6
   \]

5. **Solve for \( x \):**
   \[
   x = \frac{28.6}{4} = 7.15 \, \text{kg}
   \]

So, the baker originally had 7.15 kg of sugar.

6. **Amount of flour at first:**
   Since the amount of flour was 5 times the amount of sugar, the amount of flour was:
   \[
   5x = 5 \times 7.15 = 35.75 \, \text{kg}
   \]

Thus, the baker had **35.75 kg of flour** at first.

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### Related Questions:
1. What is the total amount of flour and sugar combined after usage?
2. How would the result change if the difference after usage were a different number?
3. If twice the amount of sugar had been used instead, what would the new difference be?
4. How can this problem be modeled using a system of equations?
5. What if the amount of sugar used was half the amount of flour used?

### Tip: 
When dealing with word problems, it's helpful to assign variables to unknown quantities and carefully express relationships as equations to avoid confusion.

A baker has some flour and sugar. At first there were 5 times as much flour than sugar. After 3.2 kg of flour and 3.2 kg of sugar were used, the difference in the amount of flour and sugar left was 28.6 kg. How much flour was there at first?

Learn how to solve an algebraic word problem involving the initial amount of flour and sugar a baker has. The problem covers key algebraic concepts like forming equations and solving for unknowns. Suitable for students in Grades 6-8.

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