18-karat gold jewelry contains 75% gold by mass. A) If the total mass of an 18-karat gold ring is 13500 mg, how many grams of gold does the ring contain? B) If an 18-karat gold bracelet contains 2.0 oz (dry) of gold, calculate the mass of the bracelet in grams
The correct answer and explanation is :
A) How many grams of gold does the 18-karat gold ring contain?
Given:
- The ring is 18-karat gold, meaning it contains 75% gold by mass.
- The total mass of the ring is 13,500 mg.
To find the mass of gold in the ring, we use the percentage of gold (75%) and apply it to the total mass of the ring.
- Convert milligrams to grams:
Since 1 gram = 1000 milligrams, we can convert the total mass of the ring from milligrams to grams. [
13,500 \, \text{mg} = \frac{13,500}{1000} = 13.5 \, \text{g}
] - Calculate the mass of gold:
The mass of gold in the ring is 75% of the total mass of the ring. To find this, we multiply the total mass (13.5 grams) by 0.75. [
\text{Mass of gold} = 0.75 \times 13.5 \, \text{g} = 10.125 \, \text{g}
]
Thus, the ring contains 10.125 grams of gold.
B) Mass of the bracelet in grams
Given:
- The bracelet contains 2.0 oz (dry) of gold.
- 1 ounce (oz) = 28.3495 grams.
To find the mass of the bracelet in grams, we need to convert the given mass in ounces to grams.
- Convert ounces to grams: [
2.0 \, \text{oz} \times 28.3495 \, \text{g/oz} = 56.699 \, \text{g}
]
Thus, the mass of the bracelet is 56.699 grams.
Explanation:
- Part A:
For the 18-karat gold ring, we are told that 18-karat gold is 75% gold by mass. This means that for every 100 grams of the jewelry, 75 grams is pure gold. When we know the total mass of the ring is 13,500 mg (which we convert to 13.5 grams), we simply multiply this mass by the percentage of gold, which is 0.75. This gives us the mass of the gold in the ring, which is 10.125 grams. - Part B:
The bracelet’s gold content is given in ounces. Since we need the mass in grams, we convert ounces to grams by using the conversion factor 1 ounce = 28.3495 grams. Multiplying 2.0 ounces by this factor gives us the bracelet’s total mass in grams, which is 56.699 grams.
In both cases, the essential idea is to use percentages or unit conversions to convert the given information into the desired mass unit (grams).