Answer :
- Set up the equation: $\frac{7}{8}x = 224$, where $x$ is the weight Balin can bench press.
- Multiply both sides by $\frac{8}{7}$ to isolate $x$: $x = 224 \times \frac{8}{7}$.
- Calculate the value of $x$: $x = \frac{1792}{7}$.
- Find the final value: $x = \boxed{256}$ pounds.
### Explanation
1. Understanding the Problem
Let's analyze the problem. We know that Jasper can bench press 224 pounds, and this is $\frac{7}{8}$ of the weight that Balin can bench press. We need to find the correct equation and the value of $x$, which represents the weight Balin can bench press.
2. Setting up the Equation
We can set up the equation as follows: $\frac{7}{8}$ of Balin's weight ($x$) is equal to Jasper's weight (224 pounds). This translates to the equation $\frac{7}{8}x = 224$.
3. Isolating x
To solve for $x$, we need to isolate $x$ by multiplying both sides of the equation by the reciprocal of $\frac{7}{8}$, which is $\frac{8}{7}$. So, we have: $$x = 224 \times \frac{8}{7}$$
4. Calculating x
Now, let's calculate the value of $x$: $$x = \frac{224 \times 8}{7} = \frac{1792}{7}$$
5. Finding the Value of x
Performing the division, we find: $$x = 256$$
6. Conclusion
Therefore, the correct equation is $\frac{7}{8}x = 224$, and the value of $x$ is 256 pounds.
### Examples
Understanding fractions and equations like this is useful in many real-life situations. For example, if you are baking and need to adjust a recipe, or if you are calculating discounts while shopping, you'll use similar math skills. Also, understanding proportions is essential in fields like engineering, where scaling models and understanding ratios are crucial.
- Multiply both sides by $\frac{8}{7}$ to isolate $x$: $x = 224 \times \frac{8}{7}$.
- Calculate the value of $x$: $x = \frac{1792}{7}$.
- Find the final value: $x = \boxed{256}$ pounds.
### Explanation
1. Understanding the Problem
Let's analyze the problem. We know that Jasper can bench press 224 pounds, and this is $\frac{7}{8}$ of the weight that Balin can bench press. We need to find the correct equation and the value of $x$, which represents the weight Balin can bench press.
2. Setting up the Equation
We can set up the equation as follows: $\frac{7}{8}$ of Balin's weight ($x$) is equal to Jasper's weight (224 pounds). This translates to the equation $\frac{7}{8}x = 224$.
3. Isolating x
To solve for $x$, we need to isolate $x$ by multiplying both sides of the equation by the reciprocal of $\frac{7}{8}$, which is $\frac{8}{7}$. So, we have: $$x = 224 \times \frac{8}{7}$$
4. Calculating x
Now, let's calculate the value of $x$: $$x = \frac{224 \times 8}{7} = \frac{1792}{7}$$
5. Finding the Value of x
Performing the division, we find: $$x = 256$$
6. Conclusion
Therefore, the correct equation is $\frac{7}{8}x = 224$, and the value of $x$ is 256 pounds.
### Examples
Understanding fractions and equations like this is useful in many real-life situations. For example, if you are baking and need to adjust a recipe, or if you are calculating discounts while shopping, you'll use similar math skills. Also, understanding proportions is essential in fields like engineering, where scaling models and understanding ratios are crucial.
