Answer :
- Set up the equation representing the problem: $\frac{7}{8}x = 224$.
- Multiply both sides by $\frac{8}{7}$ to isolate $x$: $x = 224 \times \frac{8}{7}$.
- Calculate the value of $x$: $x = \frac{1792}{7}$.
- Simplify to find the weight Balin can bench press: $x = \boxed{256}$ pounds.
### Explanation
1. Understanding the Problem
Let's analyze the problem. We know that Jasper bench presses 224 pounds, and this is $\frac{7}{8}$ of what Balin bench presses. We need to find the correct equation and the weight Balin bench presses, which we'll call $x$.
2. Setting up the Equation
We can set up the equation: $\frac{7}{8}$ 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: $x = 224 \cdot \frac{8}{7}$.
4. Calculating x
Now, let's calculate the value of $x$: $x = \frac{224 \times 8}{7} = \frac{1792}{7}$.
5. Finding the Answer
Simplifying the fraction, we get $x = 256$. Therefore, Balin can bench press 256 pounds.
6. Conclusion
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're baking and need to adjust a recipe, or if you're calculating discounts while shopping, setting up and solving equations with fractions is essential. Imagine you're buying a shirt that's 25% off, and the sale price is $30. You can use a similar equation to figure out the original price of the shirt. These skills help in making informed decisions every day.
- Multiply both sides by $\frac{8}{7}$ to isolate $x$: $x = 224 \times \frac{8}{7}$.
- Calculate the value of $x$: $x = \frac{1792}{7}$.
- Simplify to find the weight Balin can bench press: $x = \boxed{256}$ pounds.
### Explanation
1. Understanding the Problem
Let's analyze the problem. We know that Jasper bench presses 224 pounds, and this is $\frac{7}{8}$ of what Balin bench presses. We need to find the correct equation and the weight Balin bench presses, which we'll call $x$.
2. Setting up the Equation
We can set up the equation: $\frac{7}{8}$ 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: $x = 224 \cdot \frac{8}{7}$.
4. Calculating x
Now, let's calculate the value of $x$: $x = \frac{224 \times 8}{7} = \frac{1792}{7}$.
5. Finding the Answer
Simplifying the fraction, we get $x = 256$. Therefore, Balin can bench press 256 pounds.
6. Conclusion
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're baking and need to adjust a recipe, or if you're calculating discounts while shopping, setting up and solving equations with fractions is essential. Imagine you're buying a shirt that's 25% off, and the sale price is $30. You can use a similar equation to figure out the original price of the shirt. These skills help in making informed decisions every day.
