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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{1}{224}; \, x = 256[/tex] pounds

Answer :

To solve the problem, we want to find out how much weight Balin can bench press, given that 224 pounds is [tex]\(\frac{7}{8}\)[/tex] of that weight. We can set up the equation and solve for [tex]\(x\)[/tex], which represents the weight that Balin can bench press.

1. Set up the equation:

The problem states that 224 pounds is [tex]\(\frac{7}{8}\)[/tex] of Balin's weight, so we write:

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

2. Solve for [tex]\(x\)[/tex]:

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

3. Calculate the value:

Perform the multiplication:

[tex]\[
x = 256
\][/tex]

So, Balin can bench press 256 pounds. Therefore, the correct answer is:

[tex]\(\frac{7}{8} x = 224, x = 256\)[/tex] pounds.

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