Answer :
To solve the problem, we need to determine the weight that Balin could bench press. We are given that Jasper was able to bench press 224 pounds, which is [tex]\(\frac{7}{8}\)[/tex] of the weight that Balin could bench press.
Let's break it down step-by-step:
1. Identify the relationship: We know that [tex]\(\frac{7}{8}\)[/tex] of Balin's weight equals 224 pounds. We can express this relationship with an equation where [tex]\(x\)[/tex] represents the weight Balin could bench press:
[tex]\[
\frac{7}{8}x = 224
\][/tex]
2. Solve for [tex]\(x\)[/tex]: To find the value of [tex]\(x\)[/tex], we need to isolate it. We can do this by multiplying 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 result: Perform the multiplication to find the value of [tex]\(x\)[/tex].
[tex]\[
x = 224 \times \frac{8}{7} = 256
\][/tex]
Therefore, the correct equation and value of [tex]\(x\)[/tex], the weight that Balin could bench press, is:
[tex]\[
\frac{7}{8}x = 224; \, x = 256 \text{ pounds}
\][/tex]
This matches the option: [tex]\(\frac{7}{8}x = 224; x = 256\)[/tex] pounds.
Let's break it down step-by-step:
1. Identify the relationship: We know that [tex]\(\frac{7}{8}\)[/tex] of Balin's weight equals 224 pounds. We can express this relationship with an equation where [tex]\(x\)[/tex] represents the weight Balin could bench press:
[tex]\[
\frac{7}{8}x = 224
\][/tex]
2. Solve for [tex]\(x\)[/tex]: To find the value of [tex]\(x\)[/tex], we need to isolate it. We can do this by multiplying 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 result: Perform the multiplication to find the value of [tex]\(x\)[/tex].
[tex]\[
x = 224 \times \frac{8}{7} = 256
\][/tex]
Therefore, the correct equation and value of [tex]\(x\)[/tex], the weight that Balin could bench press, is:
[tex]\[
\frac{7}{8}x = 224; \, x = 256 \text{ pounds}
\][/tex]
This matches the option: [tex]\(\frac{7}{8}x = 224; x = 256\)[/tex] pounds.
