To solve the problem of dividing 3000 grams in the ratio of 1:2, let's break this down into clear steps.
1. Identify the total number of parts in the ratio:
- The given ratio is 1:2, which means 1 part for one quantity and 2 parts for the other.
- To find the total number of parts, add the parts in the ratio:
[tex]\[
\text{Total parts} = 1 + 2 = 3
\][/tex]
2. Determine the weight corresponding to each part:
- The total amount to be divided is 3000 grams.
- Each part of the ratio is an equal fraction of the total amount.
- To find the weight of one part, divide the total amount by the total number of parts:
[tex]\[
1 \text{ part} = \frac{3000 \text{ grams}}{3} = 1000 \text{ grams}
\][/tex]
3. Calculate the amounts for each quantity in the ratio:
- Since the first quantity gets 1 part, it will be:
[tex]\[
\text{Amount for the first quantity} = 1 \times 1000 \text{ grams} = 1000 \text{ grams}
\][/tex]
- The second quantity gets 2 parts, so it will be:
[tex]\[
\text{Amount for the second quantity} = 2 \times 1000 \text{ grams} = 2000 \text{ grams}
\][/tex]
4. Conclusion with the divided weights:
- Thus, when you divide 3000 grams in the ratio of 1:2, you get:
[tex]\[
\text{First quantity}: 1000 \text{ grams} \\
\text{Second quantity}: 2000 \text{ grams}
\][/tex]
So, the 3000 grams divided in the ratio 1:2 results in 1000 grams for the first quantity and 2000 grams for the second quantity.
