Final answer:
To solve the given equation 3 1/X * 5 1/4 = 17 1/2, convert the mixed numbers into improper fractions. Cross multiply to eliminate the fractions. Simplify the equation and solve for X. The solution is X = 2/15.
Step-by-step explanation:
To solve the given equation: 3 1/X * 5 1/4 = 17 1/2
First, convert the mixed numbers into improper fractions. 3 1/X can be written as (3X + 1)/X, and 5 1/4 can be written as (5*4 + 1)/4 = 21/4.
The equation now becomes: (3X + 1)/X * 21/4 = 17 1/2.
To eliminate the fractions, you can cross multiply: (3X + 1)(2) = X(21).
Simplify the equation: 6X + 2 = 21X.
Combine like terms: 6X - 21X = -2.
Subtract 6X from both sides: -15X = -2.
Divide by -15: X = -2/-15.
X simplifies to 2/15.
So, the solution to the equation is X = 2/15.