Let's solve the equation step-by-step to find the value of [tex]\( m \)[/tex] when [tex]\( n \)[/tex] is given as 20.
Given equation:
[tex]\[
\frac{1}{2}m - \frac{3}{4}n = 16
\][/tex]
Let's follow the steps to solve for [tex]\( m \)[/tex].
### Step 1: Simplify the Equation
First, we'll eliminate the fractions by multiplying the entire equation by 4:
[tex]\[
4 \left( \frac{1}{2}m - \frac{3}{4}n \right) = 4 \cdot 16
\][/tex]
This gives us:
[tex]\[
2m - 3n = 64
\][/tex]
### Step 2: Substitute the Value of [tex]\( n \)[/tex]
We are given [tex]\( n = 20 \)[/tex]. Substitute this value into the equation:
[tex]\[
2m - 3(20) = 64
\][/tex]
### Step 3: Simplify the Equation Further
Calculate [tex]\( 3 \times 20 \)[/tex]:
[tex]\[
2m - 60 = 64
\][/tex]
### Step 4: Isolate the term containing [tex]\( m \)[/tex]
Add 60 to both sides to isolate the [tex]\( 2m \)[/tex] term:
[tex]\[
2m = 64 + 60
\][/tex]
This simplifies to:
[tex]\[
2m = 124
\][/tex]
### Step 5: Solve for [tex]\( m \)[/tex]
Finally, divide both sides by 2 to solve for [tex]\( m \)[/tex]:
[tex]\[
m = \frac{124}{2}
\][/tex]
So, the value of [tex]\( m \)[/tex] is:
[tex]\[
m = 62
\][/tex]
Therefore, the value of [tex]\( m \)[/tex] when [tex]\( n = 20 \)[/tex] is [tex]\( \boxed{62} \)[/tex].
