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 sugar were used, the difference in the amount of flour and sugar left was 28.6 kg. how much flour was there at first? what was the total amount of flour and sugar left?

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

After using 3.2 kg of both flour and sugar, the baker had \( 5x - 3.2 \) kg of flour and \( x - 3.2 \) kg of sugar remaining.

According to the problem, the difference between the remaining amount of flour and sugar is 28.6 kg. Therefore, we can set up the equation:

\[
(5x - 3.2) - (x - 3.2) = 28.6
\]

Simplifying the equation:

\[
5x - 3.2 - x + 3.2 = 28.6
\]

\[
4x = 28.6
\]

Solving for \( x \):

\[
x = \frac{28.6}{4} = 7.15
\]

So, the baker originally had 7.15 kg of sugar. The initial amount of flour was:

\[
5x = 5 \times 7.15 = 35.75 \text{ kg of flour.}
\]

Now, let's calculate how much flour and sugar was left after using 3.2 kg of each:

- Amount of flour left: \( 35.75 - 3.2 = 32.55 \text{ kg} \)
- Amount of sugar left: \( 7.15 - 3.2 = 3.95 \text{ kg} \)

Thus, the total amount of flour and sugar left is:

\[
32.55 + 3.95 = 36.5 \text{ kg.}
\]

### Final Answers:
- The baker had 35.75 kg of flour at first.
- The total amount of flour and sugar left is 36.5 kg.

Would you like further details or have any questions?

Here are some related questions:
1. What if the baker had used 5 kg of both flour and sugar instead of 3.2 kg?
2. How much sugar would be left if the initial sugar amount was doubled?
3. What if the difference between the remaining flour and sugar was 50 kg instead of 28.6 kg?
4. How would the amounts change if the baker used half as much flour and sugar?
5. What would happen if the baker started with 10 times as much flour as sugar?

**Tip:** When solving word problems, carefully translate each part of the problem into an equation based on given relationships.

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

Learn how to solve a real-world word problem involving flour and sugar using linear equations. The problem involves basic algebra and is suitable for students in Grades 6-8. It covers solving for unknowns, simplifying expressions, and understanding word problems.

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