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 bench 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

To solve this problem, we need to find out how much weight Balin could bench press, given that Jasper could bench press 224 pounds, which is [tex]$\frac{7}{8}$[/tex] of Balin's weight.

1. Understand the relationship: We know that Jasper's bench press weight is [tex]$\frac{7}{8}$[/tex] of Balin's weight. This can be written as the equation:
[tex]\[
\frac{7}{8} \times x = 224
\][/tex]
where [tex]$x$[/tex] is the weight Balin could bench press.

2. Solve the equation: To find [tex]$x$[/tex], we need to isolate it. 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]

3. Simplify the division: Dividing by a fraction is the same as multiplying by its reciprocal. So, we have:
[tex]\[
x = 224 \times \frac{8}{7}
\][/tex]

4. Calculate the result: Perform the multiplication:
[tex]\[
x = 224 \times \frac{8}{7} = 256
\][/tex]

So, Balin could bench press 256 pounds.

The correct equation and value of [tex]$x$[/tex] is:
[tex]\[
\frac{7}{8} x = 224; \, x = 256 \, \text{pounds}
\][/tex]

Therefore, the correct option from the choices provided is:
[tex]\[
\frac{7}{8} x = 224 ; x = 256 \, \text{pounds}
\][/tex]