Problem: Find x if 9/4:x=3/11:5/33.

Solution:

To solve for x, we will use the concept of cross-multiplication. Cross-multiplication is a method of solving proportions by multiplying the numerator of one ratio by the denominator of the other ratio and setting the two products equal to each other.

The given proportion is:

9/4:x = 3/11:5/33

We can cross-multiply the terms to get:

(9/4) * (5/33) = (3/11) * x

Simplifying the left-hand side, we get:

(9/4) * (5/33) = 15/44

Now, we can solve for x by isolating it on one side of the equation:

(3/11) * x = 15/44

Multiplying both sides by 11/3, we get:

x = (15/44) * (11/3)

Simplifying, we get:

x = 5/4

Therefore, the value of x is 5/4.

Answer: x = 5/4

(9/4) : x = (3/11) : (5/33)

(9/4) : x = (3 * 33)/(11 * 5)

x = (3 * 33 * 9)/(11 * 5 * 4)

x = (3 * 3 * 9)/(5 * 4)

x = 81/20 (Ans)