Answer :
To determine the weight that Balin could bench press, we start by using the information given in the problem:
1. Jasper was able to bench press 224 pounds.
2. This weight is [tex]\(\frac{7}{8}\)[/tex] of the weight Balin could bench press.
We can set up the equation to represent this relationship:
[tex]\[
\frac{7}{8} \times x = 224
\][/tex]
Here, [tex]\(x\)[/tex] represents the weight that Balin could bench press.
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 of the equation 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. The reciprocal of [tex]\(\frac{7}{8}\)[/tex] is [tex]\(\frac{8}{7}\)[/tex]. So, we rewrite the equation:
[tex]\[
x = 224 \times \frac{8}{7}
\][/tex]
When we multiply 224 by [tex]\(\frac{8}{7}\)[/tex], we get:
[tex]\[
x = 256
\][/tex]
Therefore, the correct equation and value of [tex]\(x\)[/tex], the weight that Balin could bench press, is:
[tex]\[
\frac{7}{8} x = 224 \quad ; \quad x = 256 \text{ pounds}
\][/tex]
Thus, the correct choice is:
[tex]\[
\frac{7}{8} x = 224 ; x = 256 \text{ pounds}
\][/tex]
1. Jasper was able to bench press 224 pounds.
2. This weight is [tex]\(\frac{7}{8}\)[/tex] of the weight Balin could bench press.
We can set up the equation to represent this relationship:
[tex]\[
\frac{7}{8} \times x = 224
\][/tex]
Here, [tex]\(x\)[/tex] represents the weight that Balin could bench press.
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 of the equation 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. The reciprocal of [tex]\(\frac{7}{8}\)[/tex] is [tex]\(\frac{8}{7}\)[/tex]. So, we rewrite the equation:
[tex]\[
x = 224 \times \frac{8}{7}
\][/tex]
When we multiply 224 by [tex]\(\frac{8}{7}\)[/tex], we get:
[tex]\[
x = 256
\][/tex]
Therefore, the correct equation and value of [tex]\(x\)[/tex], the weight that Balin could bench press, is:
[tex]\[
\frac{7}{8} x = 224 \quad ; \quad x = 256 \text{ pounds}
\][/tex]
Thus, the correct choice is:
[tex]\[
\frac{7}{8} x = 224 ; x = 256 \text{ pounds}
\][/tex]
