Answer :
To solve this problem, we are given that Jasper was able to bench press 224 pounds, which was [tex]\(\frac{7}{8}\)[/tex] of the weight that Balin could bench press. We need to find the equation and the value of [tex]\(x\)[/tex], representing the weight that Balin could bench press.
Let's break it down step by step:
1. Understand the Relationship:
- We know [tex]\(\frac{7}{8}\)[/tex] of Balin's bench press weight equals Jasper's bench press weight of 224 pounds.
2. Set Up the Equation:
- The equation for this scenario is [tex]\(\frac{7}{8} \times x = 224\)[/tex], where [tex]\(x\)[/tex] is the weight Balin could bench press.
3. Solve for [tex]\(x\)[/tex]:
- To find [tex]\(x\)[/tex], we need to isolate it in the equation. We can do this by multiplying both sides by the reciprocal of [tex]\(\frac{7}{8}\)[/tex], which is [tex]\(\frac{8}{7}\)[/tex].
4. Calculate:
[tex]\[
x = 224 \times \frac{8}{7}
\][/tex]
5. Simplify:
- Perform the multiplication:
[tex]\[
x = \frac{224 \times 8}{7} = \frac{1792}{7} = 256
\][/tex]
So, the correct equation and value of [tex]\(x\)[/tex] are [tex]\((\frac{7}{8})x = 224\)[/tex], and [tex]\(x = 256\)[/tex] pounds.
The correct choice from the options given would be:
[tex]\(\frac{7}{8} x = 224 ; x = 256\)[/tex] pounds.
Let's break it down step by step:
1. Understand the Relationship:
- We know [tex]\(\frac{7}{8}\)[/tex] of Balin's bench press weight equals Jasper's bench press weight of 224 pounds.
2. Set Up the Equation:
- The equation for this scenario is [tex]\(\frac{7}{8} \times x = 224\)[/tex], where [tex]\(x\)[/tex] is the weight Balin could bench press.
3. Solve for [tex]\(x\)[/tex]:
- To find [tex]\(x\)[/tex], we need to isolate it in the equation. We can do this by multiplying both sides by the reciprocal of [tex]\(\frac{7}{8}\)[/tex], which is [tex]\(\frac{8}{7}\)[/tex].
4. Calculate:
[tex]\[
x = 224 \times \frac{8}{7}
\][/tex]
5. Simplify:
- Perform the multiplication:
[tex]\[
x = \frac{224 \times 8}{7} = \frac{1792}{7} = 256
\][/tex]
So, the correct equation and value of [tex]\(x\)[/tex] are [tex]\((\frac{7}{8})x = 224\)[/tex], and [tex]\(x = 256\)[/tex] pounds.
The correct choice from the options given would be:
[tex]\(\frac{7}{8} x = 224 ; x = 256\)[/tex] pounds.
