Answer :
Let's solve the problem step by step:
1. Understand the problem:
Jasper was able to bench press 224 pounds, which is [tex]\(\frac{7}{8}\)[/tex] of the weight that Balin can bench press. We need to find the total weight that Balin can bench press, represented by [tex]\(x\)[/tex].
2. Set up the equation:
The equation we have is [tex]\(\frac{7}{8} \times x = 224\)[/tex]. This represents the relationship between Jasper’s and Balin’s bench pressing weights, where [tex]\(\frac{7}{8}\)[/tex] of Balin's weight is equal to 224 pounds.
3. Solve for [tex]\(x\)[/tex]:
To find [tex]\(x\)[/tex], we need to solve the equation [tex]\(\frac{7}{8} \times x = 224\)[/tex]. We do this by dividing both sides of the equation by [tex]\(\frac{7}{8}\)[/tex].
[tex]\[
x = \frac{224}{\frac{7}{8}}
\][/tex]
Simplifying the division, we know dividing by a fraction is the same as multiplying by its reciprocal:
[tex]\[
x = 224 \times \frac{8}{7}
\][/tex]
Calculating that gives:
[tex]\[
x = 256
\][/tex]
4. Conclusion:
The weight that Balin can bench press is 256 pounds. Therefore, the correct equation and value for [tex]\(x\)[/tex] is [tex]\(\frac{7}{8} x = 224 ; x = 256\)[/tex] pounds.
The choice that corresponds with this solution is:
[tex]\(\frac{7}{8} x=224 ; x=256\)[/tex] pounds.
1. Understand the problem:
Jasper was able to bench press 224 pounds, which is [tex]\(\frac{7}{8}\)[/tex] of the weight that Balin can bench press. We need to find the total weight that Balin can bench press, represented by [tex]\(x\)[/tex].
2. Set up the equation:
The equation we have is [tex]\(\frac{7}{8} \times x = 224\)[/tex]. This represents the relationship between Jasper’s and Balin’s bench pressing weights, where [tex]\(\frac{7}{8}\)[/tex] of Balin's weight is equal to 224 pounds.
3. Solve for [tex]\(x\)[/tex]:
To find [tex]\(x\)[/tex], we need to solve the equation [tex]\(\frac{7}{8} \times x = 224\)[/tex]. We do this by dividing both sides of the equation by [tex]\(\frac{7}{8}\)[/tex].
[tex]\[
x = \frac{224}{\frac{7}{8}}
\][/tex]
Simplifying the division, we know dividing by a fraction is the same as multiplying by its reciprocal:
[tex]\[
x = 224 \times \frac{8}{7}
\][/tex]
Calculating that gives:
[tex]\[
x = 256
\][/tex]
4. Conclusion:
The weight that Balin can bench press is 256 pounds. Therefore, the correct equation and value for [tex]\(x\)[/tex] is [tex]\(\frac{7}{8} x = 224 ; x = 256\)[/tex] pounds.
The choice that corresponds with this solution is:
[tex]\(\frac{7}{8} x=224 ; x=256\)[/tex] pounds.
