A dog's original eight was 2.6 pounds. After 10 weeks the dogs weighed 1 1/3 it's original weight. How much did the dog weigh after 10 weeks.

The weight of the dog, having initial weight of 2.6 pounds, after 10 weeks is found to be 3.47 pounds.

Step-by-step explanation:

This problem can be solved using equation having one variable. This is explained below.

1. The equation will involve a single variable on the left side of the equal sign and an expression which needs to be evaluated, on the right side of the equal sign.

2. The initial weight of the dog is given as 2.6 pounds.

3. The weight of the dog after 10 weeks needs to be found out.

4. The change in weight of the dog after 10 weeks is given by 1/frac{1}{3}, which can also be written as / frac{4}{3}, of the original weight.

5. The equation will be formed to determine the new weight after 10 weeks which is equated to the original weight multiplied by / frac{4}{3}.

6. Let the new weight of the dog after 10 weeks be denoted by variable w.

7. The variable, w, will appear on the left side of the equal sign.

8. The expression to evaluate the new weight after 10 weeks is taken on the right side of the equal sign.

9. The equation in one variable, w, can be written as follows.

w = 2.6 / times / frac{4}{3}

10. The fraction is simplified and written with two decimal places.

11. The right side of the equation now contains two numbers with decimal places.

w = 2.6 / times 1.33

12. The expression on the right side of the equal sign is simplified to get the value of new weight.

w = 3.47

13. Hence, the new weight of the dog after 10 weeks is / frac{4}{3} of the original weight, 2.6 pounds, and is determined to be 3.47 pounds.

The problems in which one value is given and other related value needs to be found out, can be solved using equation having one variable method as explained above.