Answer :
Sure! Let's solve the problem step-by-step.
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. We need to find the weight [tex]\( x \)[/tex] that Balin could bench press.
The given equation is:
[tex]\[ \frac{7}{8} x = 224 \][/tex]
To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex] on one side of the equation. Here are the steps:
1. Multiply both sides of the equation by the reciprocal of [tex]\(\frac{7}{8}\)[/tex]:
The reciprocal of [tex]\(\frac{7}{8}\)[/tex] is [tex]\(\frac{8}{7}\)[/tex].
So, we multiply both sides of the equation by [tex]\(\frac{8}{7}\)[/tex]:
[tex]\[
\left(\frac{8}{7}\right) \left(\frac{7}{8} x\right) = 224 \times \left(\frac{8}{7}\right)
\][/tex]
2. Simplify the left side of the equation:
[tex]\[
\left(\frac{8}{7} \times \frac{7}{8}\right) x = 224 \times \frac{8}{7}
\][/tex]
The left side simplifies to:
[tex]\[
1 \cdot x = x
\][/tex]
3. Calculate the right side of the equation:
[tex]\[
224 \times \frac{8}{7} = 256
\][/tex]
So, [tex]\( x = 256 \)[/tex].
Therefore, the weight that Balin could bench press is 256 pounds.
This matches with the option:
[tex]\[ \frac{7}{8} x = 224 ; x = 256 \text{ pounds} \][/tex]
Answer: [tex]\(\boxed{\frac{7}{8} x = 224 ; x = 256 \text{ pounds}}\)[/tex]
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. We need to find the weight [tex]\( x \)[/tex] that Balin could bench press.
The given equation is:
[tex]\[ \frac{7}{8} x = 224 \][/tex]
To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex] on one side of the equation. Here are the steps:
1. Multiply both sides of the equation by the reciprocal of [tex]\(\frac{7}{8}\)[/tex]:
The reciprocal of [tex]\(\frac{7}{8}\)[/tex] is [tex]\(\frac{8}{7}\)[/tex].
So, we multiply both sides of the equation by [tex]\(\frac{8}{7}\)[/tex]:
[tex]\[
\left(\frac{8}{7}\right) \left(\frac{7}{8} x\right) = 224 \times \left(\frac{8}{7}\right)
\][/tex]
2. Simplify the left side of the equation:
[tex]\[
\left(\frac{8}{7} \times \frac{7}{8}\right) x = 224 \times \frac{8}{7}
\][/tex]
The left side simplifies to:
[tex]\[
1 \cdot x = x
\][/tex]
3. Calculate the right side of the equation:
[tex]\[
224 \times \frac{8}{7} = 256
\][/tex]
So, [tex]\( x = 256 \)[/tex].
Therefore, the weight that Balin could bench press is 256 pounds.
This matches with the option:
[tex]\[ \frac{7}{8} x = 224 ; x = 256 \text{ pounds} \][/tex]
Answer: [tex]\(\boxed{\frac{7}{8} x = 224 ; x = 256 \text{ pounds}}\)[/tex]
