How many ounces of an alloy containing 30% gold on the world market must be added to 10 ounces of an alloy containing 5% to produce an alloy containing 20% gold?
amount of the 30% alloy to be added --- x ounces
.3x + .05(10) = .2(10+x)
.3x + .5 = 2 + .2x
.1x = 1.5
x = 15
Well, let's do a little math and a little metallurgy, shall we? To solve this problem, we can use a mixture equation.
So, we have 10 ounces of an alloy with 5% gold. Let's call this alloy "A." We also have another alloy, let's call it "B," which contains 30% gold. We need to find out how many ounces of alloy B we need to add to make an alloy with 20% gold.
Now, we know that alloy A has 5% gold, and alloy B has 30% gold. We want a final alloy with 20% gold. That means we need to find a balance between the two.
Let's say we add x ounces of alloy B to the 10 ounces of alloy A. So, after mixing, we'll have 10 + x ounces of the final alloy. The equation will look like this:
(0.05)(10) + (0.30)(x) = (0.20)(10 + x)
Now, we can solve for x:
0.5 + 0.3x = 2 + 0.2x
0.1x = 1.5
x = 15
So, to make an alloy with 20% gold, you'll need to add 15 ounces of the alloy containing 30% gold to the existing 10 ounces of the alloy containing 5% gold.
But hey, don't put all your golden eggs in one alloy!
To solve this problem, we can set up an equation using the concept of the amount of gold in each alloy.
Let's denote:
- x as the number of ounces of the alloy containing 30% gold to be added.
- (10 + x) as the total amount of the new alloy produced.
The equation based on the gold content is:
0.30x + (0.05 * 10) = 0.20(10 + x)
Let's solve this equation step by step:
Step 1: Distribute the 0.20 to the terms inside the parentheses:
0.30x + 0.05 * 10 = 2 + 0.20x
Step 2: Simplify the equation by multiplying:
0.30x + 0.50 = 2 + 0.20x
Step 3: Subtract 0.20x from both sides to isolate the x term:
0.10x + 0.50 = 2
Step 4: Subtract 0.50 from both sides to isolate the x term:
0.10x = 2 - 0.50
Step 5: Simplify:
0.10x = 1.50
Step 6: Divide both sides by 0.10 to solve for x:
x = 1.50 / 0.10
Step 7: Calculate the value:
x = 15
Therefore, you need to add 15 ounces of the alloy containing 30% gold on the world market to 10 ounces of the alloy containing 5% to produce an alloy containing 20% gold.
To find out how many ounces of the 30% gold alloy must be added, we can set up an equation based on the percentages of gold in the two alloys.
Let 'x' represent the number of ounces of the 30% gold alloy we need to add.
To calculate the amount of gold in the 10 ounces of 5% gold alloy, we multiply the weight (10 ounces) by the percentage (5%) and divide by 100:
Gold in 5% alloy = (10 ounces) * (5/100) = 0.5 ounces of gold
Since we want to end up with an alloy containing 20% gold, the total amount of gold after mixing the two alloys should be:
Gold in final alloy = (10 ounces + x ounces) * (20/100) = 0.2 * (10 + x) ounces
Now, let's equate the amount of gold in the alloys:
Gold in final alloy = Gold in 5% alloy + Gold in 30% alloy
0.2 * (10 + x) = 0.5 + 0.3x
Simplifying the equation:
2 + 0.2x = 0.5 + 0.3x
Rearranging terms:
0.3x - 0.2x = 0.5 - 2
0.1x = -1.5
Dividing by 0.1:
x = -1.5 / 0.1
x = -15
Based on the equation, we get a negative value for 'x', which doesn't make sense in this context. Therefore, it seems that the given problem is not solvable as written. Please double-check the information or the calculations to ensure the accuracy of the question.