High School

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 find out the weight that Balin could bench press, let's set up the equation based on the information given.

We know that Jasper bench pressed 224 pounds, which is [tex]\(\frac{7}{8}\)[/tex] of what Balin bench pressed. Let's call the weight that Balin bench pressed [tex]\(x\)[/tex].

The equation that represents this situation is:

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

To solve for [tex]\(x\)[/tex], we need to isolate it on one side of the equation. We can do this by dividing both sides by [tex]\(\frac{7}{8}\)[/tex]:

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

Dividing by a fraction is the same as multiplying by its reciprocal. So, we can rewrite the equation as:

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

Now, let's multiply:

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

Therefore, the weight that Balin could bench press is 256 pounds. So, the correct equation and value of [tex]\(x\)[/tex] is:

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