Sure! Let's analyze the equation and solve it step-by-step:
Given equation:
[tex]\[
\frac{13}{x} = \frac{117}{72} = \frac{y}{56}
\][/tex]
Step 1: Find the value of [tex]\(x\)[/tex]:
First, we will equate [tex]\(\frac{13}{x}\)[/tex] with [tex]\(\frac{117}{72}\)[/tex]:
[tex]\[
\frac{13}{x} = \frac{117}{72}
\][/tex]
To isolate [tex]\(x\)[/tex], we'll cross-multiply:
[tex]\[
13 \cdot 72 = 117 \cdot x
\][/tex]
This simplifies to:
[tex]\[
936 = 117x
\][/tex]
Solving for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{936}{117}
\][/tex]
Simplify the division:
[tex]\[
x = 8.0
\][/tex]
Step 2: Find the value of [tex]\(y\)[/tex]:
Next, we will equate [tex]\(\frac{117}{72}\)[/tex] with [tex]\(\frac{y}{56}\)[/tex]:
[tex]\[
\frac{117}{72} = \frac{y}{56}
\][/tex]
To isolate [tex]\(y\)[/tex], we'll cross-multiply:
[tex]\[
117 \cdot 56 = 72 \cdot y
\][/tex]
This simplifies to:
[tex]\[
6552 = 72y
\][/tex]
Solving for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{6552}{72}
\][/tex]
Simplify the division:
[tex]\[
y = 91.0
\][/tex]
Thus, the answers are:
[tex]\[
\frac{13}{8} = \frac{117}{72} = \frac{91}{56}
\][/tex]
Therefore, the blanks in the equation are filled as follows:
[tex]\[
\frac{13}{8.0} = \frac{117}{72} = \frac{91.0}{56}
\][/tex]
