Answer :
To solve this problem, we need to determine the weight that Balin could bench press, given that Jasper was able to bench press 224 pounds, which is [tex]\(\frac{7}{8}\)[/tex] of Balin's bench press weight.
Here's how you can find the solution step-by-step:
1. Let's denote the weight that Balin could bench press as [tex]\(x\)[/tex].
2. According to the problem, Jasper's bench press weight of 224 pounds is [tex]\(\frac{7}{8}\)[/tex] of Balin's weight. We can express this relationship as the equation:
[tex]\[
\frac{7}{8}x = 224
\][/tex]
3. To solve for [tex]\(x\)[/tex], we need to isolate [tex]\(x\)[/tex]. We can do this by dividing both sides of the equation by [tex]\(\frac{7}{8}\)[/tex]:
[tex]\[
x = \frac{224}{\frac{7}{8}}
\][/tex]
4. Dividing by a fraction is the same as multiplying by its reciprocal, so we rewrite the expression:
[tex]\[
x = 224 \times \frac{8}{7}
\][/tex]
5. Now, perform the multiplication:
[tex]\[
x = 224 \times \frac{8}{7} = 256
\][/tex]
So, the correct equation and value of [tex]\(x\)[/tex] (the weight that Balin could bench press) is:
[tex]\[
\frac{7}{8}x = 224 ; x = 256\text{ pounds}
\][/tex]
The correct choice from the options provided is: [tex]\(\frac{7}{8} x=224 ; x=256\)[/tex] pounds.
Here's how you can find the solution step-by-step:
1. Let's denote the weight that Balin could bench press as [tex]\(x\)[/tex].
2. According to the problem, Jasper's bench press weight of 224 pounds is [tex]\(\frac{7}{8}\)[/tex] of Balin's weight. We can express this relationship as the equation:
[tex]\[
\frac{7}{8}x = 224
\][/tex]
3. To solve for [tex]\(x\)[/tex], we need to isolate [tex]\(x\)[/tex]. We can do this by dividing both sides of the equation by [tex]\(\frac{7}{8}\)[/tex]:
[tex]\[
x = \frac{224}{\frac{7}{8}}
\][/tex]
4. Dividing by a fraction is the same as multiplying by its reciprocal, so we rewrite the expression:
[tex]\[
x = 224 \times \frac{8}{7}
\][/tex]
5. Now, perform the multiplication:
[tex]\[
x = 224 \times \frac{8}{7} = 256
\][/tex]
So, the correct equation and value of [tex]\(x\)[/tex] (the weight that Balin could bench press) is:
[tex]\[
\frac{7}{8}x = 224 ; x = 256\text{ pounds}
\][/tex]
The correct choice from the options provided is: [tex]\(\frac{7}{8} x=224 ; x=256\)[/tex] pounds.
