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

Answer :

Let [tex]$x$[/tex] be the weight (in pounds) that Balin could bench press. According to the problem, Jasper's bench press (224 pounds) is [tex]$\frac{7}{8}$[/tex] of Balin's, so we can write the equation

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

Performing the multiplication:

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

Thus, Balin could bench press 256 pounds. The correct equation and value of [tex]$x$[/tex] is:

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

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