18-carat gold is 75 percent pure, and gold ratings are proportional, you know that...
18 / 75 = 24 / x
X needs to have the same relationship to 24 that 75 has to 18.
To solve, simply cross-multiply (multiply the numerator in one fraction by the denominator in the opposite fraction, and vice versa). The resulting products will be equal. Then, simply divide away the remaining coefficient to solve for x.
18 / 75 = 24 / x
18x = 24 * 75 = 1800
x = 1800 / 18 = 100
x = 100
Therefore, the purity of 24 carat gold is 100%.