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 gold 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 your answer as a mixed number.
To find the number of grams in the positive difference between the amount of pure gold in each piece of jewelry, we need to first calculate the mass of pure gold in each piece.
For the 16-karat gold jewelry:
Since it is 16-karat gold, the fraction of pure gold in it is 16/24 = 2/3.
Therefore, the mass of pure gold in the 16-karat jewelry is (2/3) * 30 grams = 20 grams.
For the 10-karat gold jewelry:
Since it is 10-karat gold, the fraction of pure gold in it is 10/24 = 5/12.
Therefore, the mass of pure gold in the 10-karat jewelry is (5/12) * 40 grams = 50/3 grams.
Now, let's find the positive difference in grams between the two amounts of pure gold.
Positive difference = mass of pure gold in 16-karat jewelry - mass of pure gold in 10-karat jewelry
= 20 grams - 50/3 grams
To calculate this difference, we need to have a common denominator:
Positive difference = (60/3) grams - (50/3) grams
= (60 - 50)/3 grams
= 10/3 grams
Therefore, the positive difference between the amounts of pure gold in each piece of jewelry is 10/3 grams.
To express this as a mixed number, we divide the numerator (10) by the denominator (3):
10 divided by 3 equals 3 remainder 1
So the mixed number representation is:
3 1/3 grams