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

Answer :

To solve the problem, we need to determine the weight that Balin could bench press. We are given that Jasper was able to bench press 224 pounds, which is [tex]\(\frac{7}{8}\)[/tex] of the weight that Balin could bench press.

Let's break it down step-by-step:

1. Identify the relationship: We know that [tex]\(\frac{7}{8}\)[/tex] of Balin's weight equals 224 pounds. We can express this relationship with an equation where [tex]\(x\)[/tex] represents the weight Balin could bench press:
[tex]\[
\frac{7}{8}x = 224
\][/tex]

2. Solve for [tex]\(x\)[/tex]: To find the value of [tex]\(x\)[/tex], we need to isolate it. We can do this by multiplying both sides of the equation by the reciprocal of [tex]\(\frac{7}{8}\)[/tex], which is [tex]\(\frac{8}{7}\)[/tex].

[tex]\[
x = 224 \times \frac{8}{7}
\][/tex]

3. Calculate the result: Perform the multiplication to find the value of [tex]\(x\)[/tex].

[tex]\[
x = 224 \times \frac{8}{7} = 256
\][/tex]

Therefore, 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]

This matches the option: [tex]\(\frac{7}{8}x = 224; x = 256\)[/tex] pounds.