To find the weight of the gold in a 22 karat gold object, multiply the objects weight by 0.917. To find the weight of the gold in an 18 karat gold object, multiply the objects weight by 0.583. A 22 karat gold statue and a 14 karat gold statue both weigh 73.5 ounces. Which one contains more gold? How much more gold does it contain? Please help answer both questions. Thanks
22 carat has 49.1 more gold
To determine which statue contains more gold, we need to compare the weight of the gold in each statue.
Let's start by finding the weight of gold in the 22 karat gold statue. We know that the statue weighs 73.5 ounces, so we can calculate the weight of the gold as follows:
Weight of gold in the 22 karat gold statue = Weight of the statue * Percentage of gold in 22 karat gold
Weight of gold in the 22 karat gold statue = 73.5 ounces * 0.917
Weight of gold in the 22 karat gold statue = 67.3855 ounces (rounded to four decimal places)
Now let's find the weight of gold in the 14 karat gold statue. Again, we'll use the weight of the statue and the percentage of gold in 14 karat gold:
Weight of gold in the 14 karat gold statue = Weight of the statue * Percentage of gold in 14 karat gold
Weight of gold in the 14 karat gold statue = 73.5 ounces * 0.583
Weight of gold in the 14 karat gold statue = 42.7605 ounces (rounded to four decimal places)
To determine which statue contains more gold, we compare the weight of gold in each statue. In this case, the 22 karat gold statue contains more gold, as it has 67.3855 ounces compared to the 14 karat gold statue's 42.7605 ounces.
The difference in the amount of gold between the two statues can be calculated by subtracting the weight of gold in the 14 karat gold statue from the weight of gold in the 22 karat gold statue:
Difference = Weight of gold in the 22 karat gold statue - Weight of gold in the 14 karat gold statue
Difference = 67.3855 ounces - 42.7605 ounces
Difference = 24.625 ounces (rounded to three decimal places)
Therefore, the 22 karat gold statue contains 24.625 ounces more gold than the 14 karat gold statue.