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Answer :
To solve the problem of determining how much weight Balin could bench press, we start by using the information given:
Jasper can bench press 224 pounds, and this is [tex]\(\frac{7}{8}\)[/tex] of the weight that Balin can lift. We need to find the weight [tex]\(x\)[/tex] that Balin can bench press.
Here's how you solve the equation step-by-step:
1. Set up the equation: The problem states that Jasper lifts [tex]\(\frac{7}{8}\)[/tex] of Balin's weight. So, we can write the equation as:
[tex]\[
\frac{7}{8} \times x = 224
\][/tex]
2. Solve for [tex]\(x\)[/tex]: To find [tex]\(x\)[/tex], you need to isolate it on one side of the equation. You can do this by dividing both sides of the equation by [tex]\(\frac{7}{8}\)[/tex], which is equivalent to multiplying both sides 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 value of [tex]\(x\)[/tex]: Perform the multiplication:
[tex]\[
x = 224 \times \frac{8}{7} = 256
\][/tex]
So, the weight that Balin could bench press is 256 pounds. Therefore, the correct answer matches the option [tex]\(\frac{7}{8} x = 224; x = 256\)[/tex] pounds.
Jasper can bench press 224 pounds, and this is [tex]\(\frac{7}{8}\)[/tex] of the weight that Balin can lift. We need to find the weight [tex]\(x\)[/tex] that Balin can bench press.
Here's how you solve the equation step-by-step:
1. Set up the equation: The problem states that Jasper lifts [tex]\(\frac{7}{8}\)[/tex] of Balin's weight. So, we can write the equation as:
[tex]\[
\frac{7}{8} \times x = 224
\][/tex]
2. Solve for [tex]\(x\)[/tex]: To find [tex]\(x\)[/tex], you need to isolate it on one side of the equation. You can do this by dividing both sides of the equation by [tex]\(\frac{7}{8}\)[/tex], which is equivalent to multiplying both sides 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 value of [tex]\(x\)[/tex]: Perform the multiplication:
[tex]\[
x = 224 \times \frac{8}{7} = 256
\][/tex]
So, the weight that Balin could bench press is 256 pounds. Therefore, the correct answer matches the option [tex]\(\frac{7}{8} x = 224; x = 256\)[/tex] pounds.
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