The purity of gold is measured in karats. Twenty-four karat gold is pure gold and k karat gold is k/24 gold by mass. One piece of 16-karat gld jewelry has a mass of 30 grams and another piece of 10-karat gold jewelry has a mass of 40 grams. Find the number of grams in the positive difference between the amount of pure gold in each piece of jewelry. Express answer as a mixed number.

To find the difference in the amount of pure gold in each piece of jewelry, we need to calculate the mass of pure gold in each piece separately and then subtract the two masses.

First, let's find the mass of pure gold in the 16-karat jewelry piece. We know that 16-karat gold is 16/24 or 2/3 gold by mass.

Mass of 16-karat gold = (2/3) * 30 grams = 20 grams

Next, let's find the mass of pure gold in the 10-karat jewelry piece. We know that 10-karat gold is 10/24 or 5/12 gold by mass.

Mass of 10-karat gold = (5/12) * 40 grams = 16.67 grams (rounded to two decimal places)

Now, we can find the difference in the amount of pure gold between the two pieces of jewelry.

Difference in pure gold = Mass of 16-karat gold - Mass of 10-karat gold
= 20 grams - 16.67 grams
≈ 3.33 grams (rounded to two decimal places)

Therefore, the positive difference in the amount of pure gold between the pieces of jewelry is approximately 3.33 grams.