Answer :
- Establish the ratio of weights between Planet A and Planet B: $\frac{\text{Weight on Planet A}}{\text{Weight on Planet B}} = \frac{100}{3}$.
- Substitute the elephant's weight on Planet A (3700 pounds) into the ratio: $\frac{3700}{W_B} = \frac{100}{3}$.
- Solve for $W_B$ by cross-multiplication: $100 W_B = 3 \times 3700$, which simplifies to $100 W_B = 11100$.
- Divide by 100 to find the elephant's weight on Planet B: $W_B = \frac{11100}{100} = 111$. The elephant's weight on Planet B is $\boxed{111}$ pounds.
### Explanation
1. Understanding the Problem
We are given that the ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. This means that if an object weighs 100 units on Planet A, it weighs 3 units on Planet B. We can write this as a ratio: $$\frac{\text{Weight on Planet A}}{\text{Weight on Planet B}} = \frac{100}{3}$$
2. Setting up the Equation
We are also given that an elephant weighs 3700 pounds on Planet A. We want to find the elephant's weight on Planet B. Let's call the weight of the elephant on Planet B $W_B$. We can set up the following equation:$$\frac{3700}{W_B} = \frac{100}{3}$$
3. Cross-Multiplication
To solve for $W_B$, we can cross-multiply:$$100 \times W_B = 3 \times 3700$$$$100 W_B = 11100$$
4. Solving for Weight on Planet B
Now, we can divide both sides by 100 to isolate $W_B$:$$W_B = \frac{11100}{100}$$$$W_B = 111$$So, the elephant weighs 111 pounds on Planet B.
5. Final Answer
Therefore, the elephant's weight on Planet B is 111 pounds.
### Examples
Understanding ratios and proportions is crucial in many real-world scenarios. For instance, when scaling recipes, converting currencies, or calculating distances on a map, the principles of ratios and proportions come into play. In this problem, we applied these concepts to determine the weight of an object on a different planet based on a given ratio. This same approach can be used to solve various problems involving comparisons and scaling.
- Substitute the elephant's weight on Planet A (3700 pounds) into the ratio: $\frac{3700}{W_B} = \frac{100}{3}$.
- Solve for $W_B$ by cross-multiplication: $100 W_B = 3 \times 3700$, which simplifies to $100 W_B = 11100$.
- Divide by 100 to find the elephant's weight on Planet B: $W_B = \frac{11100}{100} = 111$. The elephant's weight on Planet B is $\boxed{111}$ pounds.
### Explanation
1. Understanding the Problem
We are given that the ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. This means that if an object weighs 100 units on Planet A, it weighs 3 units on Planet B. We can write this as a ratio: $$\frac{\text{Weight on Planet A}}{\text{Weight on Planet B}} = \frac{100}{3}$$
2. Setting up the Equation
We are also given that an elephant weighs 3700 pounds on Planet A. We want to find the elephant's weight on Planet B. Let's call the weight of the elephant on Planet B $W_B$. We can set up the following equation:$$\frac{3700}{W_B} = \frac{100}{3}$$
3. Cross-Multiplication
To solve for $W_B$, we can cross-multiply:$$100 \times W_B = 3 \times 3700$$$$100 W_B = 11100$$
4. Solving for Weight on Planet B
Now, we can divide both sides by 100 to isolate $W_B$:$$W_B = \frac{11100}{100}$$$$W_B = 111$$So, the elephant weighs 111 pounds on Planet B.
5. Final Answer
Therefore, the elephant's weight on Planet B is 111 pounds.
### Examples
Understanding ratios and proportions is crucial in many real-world scenarios. For instance, when scaling recipes, converting currencies, or calculating distances on a map, the principles of ratios and proportions come into play. In this problem, we applied these concepts to determine the weight of an object on a different planet based on a given ratio. This same approach can be used to solve various problems involving comparisons and scaling.
