Sure, let's solve each proportion step by step.
### Part (a)
We have the proportion:
[tex]\[ \frac{x}{6} = \frac{55}{11} \][/tex]
Step 1: Cross-multiply to clear the fraction.
[tex]\[ x \cdot 11 = 6 \cdot 55 \][/tex]
Step 2: Simplify the right side.
[tex]\[ x \cdot 11 = 330 \][/tex]
Step 3: Solve for [tex]\( x \)[/tex] by dividing both sides by 11.
[tex]\[ x = \frac{330}{11} \][/tex]
Step 4: Simplify the division.
[tex]\[ x = 30 \][/tex]
So, the value of [tex]\( x \)[/tex] in part (a) is [tex]\( 30 \)[/tex].
### Part (b)
We have the proportion:
[tex]\[ \frac{16}{18} = \frac{x}{108} \][/tex]
Step 1: Cross-multiply to clear the fraction.
[tex]\[ 16 \cdot 108 = 18 \cdot x \][/tex]
Step 2: Simplify the left side.
[tex]\[ 1728 = 18 \cdot x \][/tex]
Step 3: Solve for [tex]\( x \)[/tex] by dividing both sides by 18.
[tex]\[ x = \frac{1728}{18} \][/tex]
Step 4: Simplify the division.
[tex]\[ x = 96 \][/tex]
So, the value of [tex]\( x \)[/tex] in part (b) is [tex]\( 96 \)[/tex].
### Final Answers
(a) [tex]\( x = 30 \)[/tex]
(b) [tex]\( x = 96 \)[/tex]
