Answer :
To solve this problem, we need to determine the weight that Balin could bench press. We know Jasper can bench press 224 pounds, which is [tex]\(\frac{7}{8}\)[/tex] of the weight that Balin can lift. Let's set up an equation to find the weight, [tex]\(x\)[/tex], that Balin can bench press.
1. Understanding the problem:
- Jasper's bench press weight is 224 pounds.
- This weight represents [tex]\(\frac{7}{8}\)[/tex] of Balin's total bench press weight.
2. Setting up the equation:
- The relationship between Jasper's and Balin's weights can be expressed as:
[tex]\[
\frac{7}{8}x = 224
\][/tex]
Where [tex]\(x\)[/tex] is the weight Balin can lift.
3. Solving the equation:
- To isolate [tex]\(x\)[/tex], we need to divide both sides of the equation by [tex]\(\frac{7}{8}\)[/tex].
- Dividing by a fraction is the same as multiplying by its reciprocal. So:
[tex]\[
x = 224 \times \frac{8}{7}
\][/tex]
4. Calculate the value of [tex]\(x\)[/tex]:
- Performing the calculation:
[tex]\[
x = 224 \times \frac{8}{7} = 256
\][/tex]
5. Conclusion:
- Balin can bench press 256 pounds.
Thus, the correct equation and value of [tex]\(x\)[/tex] are:
[tex]\[
\frac{7}{8}x = 224 ; x = 256 \text{ pounds}
\][/tex]
The correct option from the choices is:
[tex]\(\frac{7}{8}x = 224; x = 256\)[/tex] pounds.
1. Understanding the problem:
- Jasper's bench press weight is 224 pounds.
- This weight represents [tex]\(\frac{7}{8}\)[/tex] of Balin's total bench press weight.
2. Setting up the equation:
- The relationship between Jasper's and Balin's weights can be expressed as:
[tex]\[
\frac{7}{8}x = 224
\][/tex]
Where [tex]\(x\)[/tex] is the weight Balin can lift.
3. Solving the equation:
- To isolate [tex]\(x\)[/tex], we need to divide both sides of the equation by [tex]\(\frac{7}{8}\)[/tex].
- Dividing by a fraction is the same as multiplying by its reciprocal. So:
[tex]\[
x = 224 \times \frac{8}{7}
\][/tex]
4. Calculate the value of [tex]\(x\)[/tex]:
- Performing the calculation:
[tex]\[
x = 224 \times \frac{8}{7} = 256
\][/tex]
5. Conclusion:
- Balin can bench press 256 pounds.
Thus, the correct equation and value of [tex]\(x\)[/tex] are:
[tex]\[
\frac{7}{8}x = 224 ; x = 256 \text{ pounds}
\][/tex]
The correct option from the choices is:
[tex]\(\frac{7}{8}x = 224; x = 256\)[/tex] pounds.
