Answer :
To solve this problem, we need to find out how much weight Balin could bench press, given that Jasper could bench press 224 pounds, which is [tex]\(\frac{7}{8}\)[/tex] of Balin's weight.
1. Understand the relationship: We know that Jasper's bench press weight is [tex]\(\frac{7}{8}\)[/tex] of Balin's weight. This can be written as the equation:
[tex]\[
\frac{7}{8} \times x = 224
\][/tex]
where [tex]\(x\)[/tex] is the weight Balin could bench press.
2. Solve the equation: To find [tex]\(x\)[/tex], we need to isolate it. 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]
3. Simplify the division: Dividing by a fraction is the same as multiplying by its reciprocal. So, we have:
[tex]\[
x = 224 \times \frac{8}{7}
\][/tex]
4. Calculate the result: Perform the multiplication:
[tex]\[
x = 224 \times \frac{8}{7} = 256
\][/tex]
So, Balin could bench press 256 pounds.
The correct equation and value of [tex]\(x\)[/tex] is:
[tex]\[
\frac{7}{8} x = 224; \, x = 256 \, \text{pounds}
\][/tex]
Therefore, the correct option from the choices provided is:
[tex]\[
\frac{7}{8} x = 224 ; x = 256 \, \text{pounds}
\][/tex]
1. Understand the relationship: We know that Jasper's bench press weight is [tex]\(\frac{7}{8}\)[/tex] of Balin's weight. This can be written as the equation:
[tex]\[
\frac{7}{8} \times x = 224
\][/tex]
where [tex]\(x\)[/tex] is the weight Balin could bench press.
2. Solve the equation: To find [tex]\(x\)[/tex], we need to isolate it. 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]
3. Simplify the division: Dividing by a fraction is the same as multiplying by its reciprocal. So, we have:
[tex]\[
x = 224 \times \frac{8}{7}
\][/tex]
4. Calculate the result: Perform the multiplication:
[tex]\[
x = 224 \times \frac{8}{7} = 256
\][/tex]
So, Balin could bench press 256 pounds.
The correct equation and value of [tex]\(x\)[/tex] is:
[tex]\[
\frac{7}{8} x = 224; \, x = 256 \, \text{pounds}
\][/tex]
Therefore, the correct option from the choices provided is:
[tex]\[
\frac{7}{8} x = 224 ; x = 256 \, \text{pounds}
\][/tex]
