a dealer has 1000kg sugar and he sells a part of it at 8% profit and the rest of it at 18% profit. The overall profit that he earns is 14%. So how much grams of the sugar did he sell at 18% profit

Let \( x \) be the amount of sugar (in kg) that the dealer sold at an 18% profit. Therefore, the amount of sugar sold at an 8% profit is \( 1000 - x \) kg.

The overall profit is given as 14%, and the total weight of sugar is 1000 kg. We can set up an equation based on the weighted average of the profits.

The total profit earned from selling \( x \) kg at 18% profit and \( 1000 - x \) kg at 8% profit can be expressed as:

\[
\text{Total profit} = \frac{\left( x \times 18 + (1000 - x) \times 8 \right)}{1000}
\]

Given that the overall profit is 14%, we set up the equation:

\[
\frac{x \times 18 + (1000 - x) \times 8}{1000} = 14
\]

Now, solve for \( x \).

### Step 1: Eliminate the denominator by multiplying both sides by 1000:

\[
x \times 18 + (1000 - x) \times 8 = 14000
\]

### Step 2: Expand both sides:

\[
18x + 8000 - 8x = 14000
\]

### Step 3: Simplify the equation:

\[
10x + 8000 = 14000
\]

### Step 4: Isolate \( x \):

\[
10x = 14000 - 8000
\]
\[
10x = 6000
\]
\[
x = 600
\]

Thus, the dealer sold **600 kg** of sugar at an 18% profit. Converting this to grams:

\[
600 \, \text{kg} = 600 \times 1000 = 600,000 \, \text{grams}
\]

So, the dealer sold **600,000 grams** of sugar at an 18% profit.

---

Would you like a detailed explanation of the steps, or do you have any questions?

Here are some related problems to consider:
1. What if the overall profit was 15% instead of 14%?
2. What would the result be if the dealer sold 400 kg at an 8% profit instead?
3. How much would the profit percentage be if all 1000 kg were sold at 8% profit?
4. What is the minimum quantity of sugar the dealer can sell at 18% profit to achieve at least 12% overall profit?
5. How would the problem change if the total sugar was 2000 kg instead of 1000 kg?

**Tip:** When dealing with weighted averages, set up equations to balance the contributions from different parts.

A dealer has 1000kg sugar and he sells a part of it at 8% profit and the rest of it at 18% profit. The overall profit that he earns is 14%. So how much grams of the sugar did he sell at 18% profit?

Solve a weighted average profit problem where a dealer sells sugar with two different profit percentages. Learn how to calculate how much sugar was sold at 18% profit given an overall profit of 14%. This problem uses key algebraic concepts and is suitable for Grades 8-10.

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