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Answer :
To solve this problem, we need to find out the weight that Balin could bench press, given that Jasper was able to lift [tex]\( \frac{7}{8} \)[/tex] of that weight, which is 224 pounds.
Let's denote the weight Balin can bench press as [tex]\( x \)[/tex].
The equation that represents this scenario is:
[tex]\[ \frac{7}{8} \times x = 224 \][/tex]
To find [tex]\( x \)[/tex], we need to solve the equation for [tex]\( x \)[/tex]. Here's how we do it step-by-step:
1. Start with the equation:
[tex]\[ \frac{7}{8} \times x = 224 \][/tex]
2. To isolate [tex]\( x \)[/tex], divide both sides of the equation by [tex]\( \frac{7}{8} \)[/tex]:
[tex]\[ x = \frac{224}{\frac{7}{8}} \][/tex]
3. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of [tex]\( \frac{7}{8} \)[/tex] is [tex]\( \frac{8}{7} \)[/tex].
4. So, multiply 224 by the reciprocal of [tex]\( \frac{7}{8} \)[/tex]:
[tex]\[ x = 224 \times \frac{8}{7} \][/tex]
5. Perform the multiplication:
[tex]\[ x = \frac{224 \times 8}{7} \][/tex]
6. Calculate the result:
[tex]\[ x = 256 \][/tex]
Therefore, the weight that Balin could bench press is 256 pounds. The correct equation and value are [tex]\(\frac{7}{8} x = 224\)[/tex] and [tex]\(x = 256\)[/tex] pounds.
Let's denote the weight Balin can bench press as [tex]\( x \)[/tex].
The equation that represents this scenario is:
[tex]\[ \frac{7}{8} \times x = 224 \][/tex]
To find [tex]\( x \)[/tex], we need to solve the equation for [tex]\( x \)[/tex]. Here's how we do it step-by-step:
1. Start with the equation:
[tex]\[ \frac{7}{8} \times x = 224 \][/tex]
2. To isolate [tex]\( x \)[/tex], divide both sides of the equation by [tex]\( \frac{7}{8} \)[/tex]:
[tex]\[ x = \frac{224}{\frac{7}{8}} \][/tex]
3. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of [tex]\( \frac{7}{8} \)[/tex] is [tex]\( \frac{8}{7} \)[/tex].
4. So, multiply 224 by the reciprocal of [tex]\( \frac{7}{8} \)[/tex]:
[tex]\[ x = 224 \times \frac{8}{7} \][/tex]
5. Perform the multiplication:
[tex]\[ x = \frac{224 \times 8}{7} \][/tex]
6. Calculate the result:
[tex]\[ x = 256 \][/tex]
Therefore, the weight that Balin could bench press is 256 pounds. The correct equation and value are [tex]\(\frac{7}{8} x = 224\)[/tex] and [tex]\(x = 256\)[/tex] pounds.
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