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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 :

We start with the fact that Jasper's bench press is [tex]$\frac{7}{8}$[/tex] of Balin's bench press. Let [tex]$x$[/tex] be the weight Balin can bench press. This relationship is written as:

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

To solve for [tex]$x$[/tex], we 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]

When you perform the multiplication, you find that:

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

Thus, the equation is [tex]$\frac{7}{8} \cdot x = 224$[/tex] and the weight [tex]$x$[/tex] that Balin could bench press is [tex]$256$[/tex] pounds.

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