In 60 ounces of alloy for watch cases there are 20 ounces of gold.how much copper must be added to the alloy so that a watch case weighing 4 ounces,made from the new alloy,will contain 1 ounce of gold.......answer is 20 ounces
To solve this problem, let's first determine the ratio of gold to alloy.
Given that there are 20 ounces of gold in 60 ounces of alloy, the ratio of gold to alloy is 20:60, which can be simplified to 1:3.
Now, let's find out how much alloy is needed to create a watch case weighing 4 ounces with 1 ounce of gold. Since the ratio of gold to alloy is 1:3, we can set up the following equation:
1 ounce of gold / 3 ounces of alloy = 1 ounce of gold / 4 ounces of alloy
Now, let's solve for the ounces of alloy needed for the new watch case:
1 / 3 = 1 / 4
Multiply both sides of the equation by 12:
4 = 3
Since the equation is not true, we can't directly use the current alloy to create the new watch case. Therefore, additional copper needs to be added to the alloy.
Now, let's find out how much copper needs to be added. Since the total weight of the new watch case is 4 ounces and we want 1 ounce of gold, the remaining weight will be for the added copper. Therefore, the amount of copper needed will be 4 - 1 = 3 ounces.
Thus, 3 ounces of copper must be added to the alloy for a watch case weighing 4 ounces, containing 1 ounce of gold.
To find out how much copper must be added, we need to understand the ratio of gold to copper in the current alloy and use it to calculate the amount of copper needed to achieve the desired ratio in the new alloy.
Let's start by finding the current ratio of gold to copper in the alloy. We know that in 60 ounces of alloy, there are 20 ounces of gold. Therefore, the ratio of gold to copper is 20:40, which simplifies to 1:2 (since 20 divided by 20 is 1 and 40 divided by 20 is 2).
Now, we need to determine how much copper is needed to achieve the desired ratio in the new alloy. Since we want a watch case weighing 4 ounces to contain 1 ounce of gold, the desired ratio is 1:3 (1 ounce of gold to 3 ounces of alloy). Since we already have 1 ounce of gold in the new alloy, we need to add enough copper to match the desired ratio.
To find out how much copper is required, we compare the ratios:
Current ratio: 1:2 (gold:copper)
Desired ratio: 1:3 (gold:copper)
We can see that the copper amount needs to be multiplied by a factor of 3 to match the desired ratio. Therefore, the amount of copper needed is 2 ounces (current copper amount) multiplied by 3, which equals 6 ounces. Adding 6 ounces of copper to the new alloy will result in a total weight of 10 ounces (4 ounces of gold + 6 ounces of copper), with 1 ounce of gold in the 4-ounce watch case.
Hence, to achieve the desired ratio, 6 ounces of copper must be added to the new alloy.