Answer :
To solve the problem, we need to find out how much weight Balin can bench press. We know that Jasper can bench press 224 pounds, and this is [tex]\(\frac{7}{8}\)[/tex] of the weight that Balin can bench press.
Let's set up the equation using [tex]\(x\)[/tex] to represent the weight Balin can bench press:
[tex]\[
\frac{7}{8}x = 224
\][/tex]
To solve for [tex]\(x\)[/tex]:
1. Isolate [tex]\(x\)[/tex]: We want to get [tex]\(x\)[/tex] by itself on one side of the equation. Since [tex]\(\frac{7}{8}x\)[/tex] means [tex]\(x\)[/tex] is being multiplied by [tex]\(\frac{7}{8}\)[/tex], we can divide both sides of the equation by [tex]\(\frac{7}{8}\)[/tex] to solve for [tex]\(x\)[/tex].
[tex]\[
x = 224 \div \frac{7}{8}
\][/tex]
2. Simplify the division: Dividing by a fraction is the same as multiplying by its reciprocal. So, we multiply 224 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 result:
- First, divide 224 by 7:
[tex]\[
224 \div 7 = 32
\][/tex]
- Then, multiply the result by 8:
[tex]\[
32 \times 8 = 256
\][/tex]
Thus, the value of [tex]\(x\)[/tex], the weight that Balin can bench press, is 256 pounds. So the correct equation and value are:
[tex]\(\frac{7}{8}x = 224 ; x = 256\)[/tex] pounds.
Let's set up the equation using [tex]\(x\)[/tex] to represent the weight Balin can bench press:
[tex]\[
\frac{7}{8}x = 224
\][/tex]
To solve for [tex]\(x\)[/tex]:
1. Isolate [tex]\(x\)[/tex]: We want to get [tex]\(x\)[/tex] by itself on one side of the equation. Since [tex]\(\frac{7}{8}x\)[/tex] means [tex]\(x\)[/tex] is being multiplied by [tex]\(\frac{7}{8}\)[/tex], we can divide both sides of the equation by [tex]\(\frac{7}{8}\)[/tex] to solve for [tex]\(x\)[/tex].
[tex]\[
x = 224 \div \frac{7}{8}
\][/tex]
2. Simplify the division: Dividing by a fraction is the same as multiplying by its reciprocal. So, we multiply 224 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 result:
- First, divide 224 by 7:
[tex]\[
224 \div 7 = 32
\][/tex]
- Then, multiply the result by 8:
[tex]\[
32 \times 8 = 256
\][/tex]
Thus, the value of [tex]\(x\)[/tex], the weight that Balin can bench press, is 256 pounds. So the correct equation and value are:
[tex]\(\frac{7}{8}x = 224 ; x = 256\)[/tex] pounds.
