At the gym, Jasper was able to bench press 224 pounds, which was [tex]\frac{7}{8}[/tex] of the weight that Balin was able to press. Which shows the correct equation and value of [tex]x[/tex], the weight that Balin could bench press?

A. [tex]\frac{7}{8}x = 224; \, x = 196[/tex] pounds
B. [tex]\frac{7}{8}x = 224; \, x = 256[/tex] pounds
C. [tex]\frac{7}{8} = \frac{x}{224}; \, x = 196[/tex] pounds
D. [tex]\frac{7}{8} = \frac{x}{224}; \, x = 256[/tex] pounds

We are told that Jasper's bench press is 224 pounds and that this amount is [tex]$\frac{7}{8}$[/tex] of Balin's bench press. Let the weight that Balin can bench press be [tex]$x$[/tex]. This relationship can be written as:

[tex]$$
\frac{7}{8} \cdot x = 224.
$$[/tex]

To solve for [tex]$x$[/tex], multiply both sides of the equation by the reciprocal of [tex]$\frac{7}{8}$[/tex], which is [tex]$\frac{8}{7}$[/tex]:

[tex]$$
x = 224 \cdot \frac{8}{7}.
$$[/tex]

Performing the multiplication,

[tex]$$
x = 256.
$$[/tex]

Thus, the correct equation is

[tex]$$
\frac{7}{8} \cdot x = 224 \quad \text{and} \quad x = 256 \text{ pounds}.
$$[/tex]

So, the answer is the option:

[tex]$$\frac{7}{8} x=224 ; x=256 \text{ pounds}.$$[/tex]