Answer :
- Set up the equation: $\frac{7}{8}x = 224$.
- Multiply both sides by $\frac{8}{7}$ to isolate $x$.
- Calculate $x = 224 \times \frac{8}{7}$.
- The weight Balin could bench press is $\boxed{256}$ pounds.
### Explanation
1. Problem Analysis
Let's analyze the problem. We are given that Jasper's bench press weight is 224 pounds, and this is $\frac{7}{8}$ of Balin's bench press weight. We need to find the correct equation and the value of $x$, which represents Balin's bench press weight.
2. Setting up the Equation
We can set up the equation as $\frac{7}{8}x = 224$, where $x$ is Balin's bench press weight. This equation states that $\frac{7}{8}$ of Balin's weight is equal to Jasper's weight, which is 224 pounds.
3. Solving for x
To solve for $x$, we need to multiply both sides of the equation by the reciprocal of $\frac{7}{8}$, which is $\frac{8}{7}$. So, we have:
$$x = 224 \times \frac{8}{7}$$
$$x = \frac{224 \times 8}{7}$$
$$x = \frac{1792}{7}$$
$$x = 256$$
4. Finding the Answer
Therefore, Balin's bench press weight is 256 pounds. The correct equation is $\frac{7}{8}x = 224$, and the value of $x$ is 256.
### Examples
Understanding fractions and proportions is crucial in everyday life. For instance, when you're baking, you often need to adjust ingredient quantities based on a recipe. If a recipe calls for $\frac{2}{3}$ cup of flour and you only want to make half the recipe, you need to calculate $\frac{1}{2}$ of $\frac{2}{3}$, which is $\frac{1}{3}$ cup. This problem demonstrates how proportional relationships help in scaling recipes accurately, ensuring your baked goods turn out perfectly every time.
- Multiply both sides by $\frac{8}{7}$ to isolate $x$.
- Calculate $x = 224 \times \frac{8}{7}$.
- The weight Balin could bench press is $\boxed{256}$ pounds.
### Explanation
1. Problem Analysis
Let's analyze the problem. We are given that Jasper's bench press weight is 224 pounds, and this is $\frac{7}{8}$ of Balin's bench press weight. We need to find the correct equation and the value of $x$, which represents Balin's bench press weight.
2. Setting up the Equation
We can set up the equation as $\frac{7}{8}x = 224$, where $x$ is Balin's bench press weight. This equation states that $\frac{7}{8}$ of Balin's weight is equal to Jasper's weight, which is 224 pounds.
3. Solving for x
To solve for $x$, we need to multiply both sides of the equation by the reciprocal of $\frac{7}{8}$, which is $\frac{8}{7}$. So, we have:
$$x = 224 \times \frac{8}{7}$$
$$x = \frac{224 \times 8}{7}$$
$$x = \frac{1792}{7}$$
$$x = 256$$
4. Finding the Answer
Therefore, Balin's bench press weight is 256 pounds. The correct equation is $\frac{7}{8}x = 224$, and the value of $x$ is 256.
### Examples
Understanding fractions and proportions is crucial in everyday life. For instance, when you're baking, you often need to adjust ingredient quantities based on a recipe. If a recipe calls for $\frac{2}{3}$ cup of flour and you only want to make half the recipe, you need to calculate $\frac{1}{2}$ of $\frac{2}{3}$, which is $\frac{1}{3}$ cup. This problem demonstrates how proportional relationships help in scaling recipes accurately, ensuring your baked goods turn out perfectly every time.
