Answer :
To solve this problem and find out how much weight Balin could bench press, we can follow these steps:
1. Understand the relationship:
- We know that Jasper was able to bench press 224 pounds. This amount is given as [tex]\(\frac{7}{8}\)[/tex] of the weight that Balin could bench press.
2. Set up the equation:
- We denote the weight that Balin could bench press as [tex]\(x\)[/tex].
- According to the problem, [tex]\(\frac{7}{8} \times x = 224\)[/tex].
3. Solve for [tex]\(x\)[/tex]:
- To find [tex]\(x\)[/tex], we need to isolate it in the equation. This can be done by dividing both sides of the equation by [tex]\(\frac{7}{8}\)[/tex]:
[tex]\[
x = \frac{224}{\frac{7}{8}}
\][/tex]
- Dividing by a fraction is the same as multiplying by its reciprocal, so:
[tex]\[
x = 224 \times \frac{8}{7}
\][/tex]
- Calculating this gives:
[tex]\[
x = 224 \times \frac{8}{7} = 256
\][/tex]
So, Balin could bench press 256 pounds.
4. Verify with options:
- If we compare this result with the given options, the correct equation and value of [tex]\(x\)[/tex] is: [tex]\(\frac{7}{8}x = 224\)[/tex] with [tex]\(x = 256\)[/tex] pounds.
Therefore, the second option: [tex]\(\frac{7}{8}x = 224 ; x = 256\)[/tex] pounds is the correct answer.
1. Understand the relationship:
- We know that Jasper was able to bench press 224 pounds. This amount is given as [tex]\(\frac{7}{8}\)[/tex] of the weight that Balin could bench press.
2. Set up the equation:
- We denote the weight that Balin could bench press as [tex]\(x\)[/tex].
- According to the problem, [tex]\(\frac{7}{8} \times x = 224\)[/tex].
3. Solve for [tex]\(x\)[/tex]:
- To find [tex]\(x\)[/tex], we need to isolate it in the equation. This can be done by dividing both sides of the equation by [tex]\(\frac{7}{8}\)[/tex]:
[tex]\[
x = \frac{224}{\frac{7}{8}}
\][/tex]
- Dividing by a fraction is the same as multiplying by its reciprocal, so:
[tex]\[
x = 224 \times \frac{8}{7}
\][/tex]
- Calculating this gives:
[tex]\[
x = 224 \times \frac{8}{7} = 256
\][/tex]
So, Balin could bench press 256 pounds.
4. Verify with options:
- If we compare this result with the given options, the correct equation and value of [tex]\(x\)[/tex] is: [tex]\(\frac{7}{8}x = 224\)[/tex] with [tex]\(x = 256\)[/tex] pounds.
Therefore, the second option: [tex]\(\frac{7}{8}x = 224 ; x = 256\)[/tex] pounds is the correct answer.
