Question

a) $x : 7 = 9 : 21$
b) $3 : 9 = x : 81$
c) $2 : 4 = x : 20$
d) $10 : 12 = 50 : x$

Explanation:

Part a)

Step1: Use proportion property

In a proportion \( x:7 = 9:21 \), we know that \( \frac{x}{7}=\frac{9}{21} \). Cross - multiply to get \( 21x = 7\times9 \).

Step2: Solve for x

First, calculate \( 7\times9 = 63 \). Then, \( x=\frac{63}{21} \). Simplifying, we get \( x = 3 \).

Part b)

Step1: Use proportion property

For \( 3:9=x:81 \), we have \( \frac{3}{9}=\frac{x}{81} \). Cross - multiply: \( 9x = 3\times81 \).

Step2: Solve for x

Calculate \( 3\times81 = 243 \). Then, \( x=\frac{243}{9}=27 \).

Part c)

Step1: Use proportion property

For \( 2:4 = x:20 \), we have \( \frac{2}{4}=\frac{x}{20} \). Cross - multiply: \( 4x = 2\times20 \).

Step2: Solve for x

Calculate \( 2\times20 = 40 \). Then, \( x=\frac{40}{4}=10 \).

Part d)

Answer:

s:
a) \( x = 3 \)

b) \( x = 27 \)

c) \( x = 10 \)

d) \( x = 60 \)