how much copper and how much iron should be added to 100% pounds of an alloy containing 25% copper and 40% iron in order to obtain an alloy containing 30% copper and 50% iron?
If x lbs of copper and y lbs or iron are added, then we need
25 + x = .30(100+x+y)
40 + y = .50(100+x+y)
Now just solve for x and y. Be sure to check your answers.
x) 27.5
y)47.5
To solve this problem, we'll set up a system of equations. Let's start by assigning variables to represent the amounts of copper and iron to be added.
Let's say the amount of copper to be added is represented by "x" (in pounds), and the amount of iron to be added is represented by "y" (in pounds).
Given that the original alloy contains 25% copper and 40% iron, we can set up the following equation for the copper:
0.25 * 100 = 25
Similarly, for the iron content:
0.40 * 100 = 40
For the final alloy, the amount of copper should be 30% and the amount of iron should be 50%, so we can set up the following equations:
0.30 * (100 + x) = 30 + 0.25x
0.50 * (100 + y) = 50 + 0.40y
Now, we can solve this system of equations to find the values of x and y.
0.30 * (100 + x) = 30 + 0.25x
30 + 0.30x = 30 + 0.25x
0.05x = 0
x = 0
So, no additional copper (x) needs to be added.
0.50 * (100 + y) = 50 + 0.40y
50 + 0.50y = 50 + 0.40y
0.10y = 0
y = 0
Similarly, no additional iron (y) needs to be added.
Therefore, no copper or iron needs to be added to obtain an alloy containing 30% copper and 50% iron.
To find out how much copper and iron should be added, we will first need to determine the current amounts of copper and iron in the alloy containing 100 pounds. Then we can calculate the additional amounts required to achieve the desired alloy composition.
Let's start by calculating the current amounts of copper and iron in the alloy containing 100 pounds:
Copper content:
25% of 100 pounds = (25/100) * 100 = 25 pounds
Iron content:
40% of 100 pounds = (40/100) * 100 = 40 pounds
Next, let's determine the desired amounts of copper and iron in the final alloy:
Copper content:
30% of (100 + additional pounds) = (30/100) * (100 + additional pounds)
Iron content:
50% of (100 + additional pounds) = (50/100) * (100 + additional pounds)
To balance the copper and iron percentages, the equation is as follows:
(30/100) * (100 + additional pounds) = (50/100) * (100 + additional pounds)
Now, let's solve this equation to find the additional pounds needed:
(30/100) * (100 + additional pounds) = (50/100) * (100 + additional pounds)
30 * (100 + additional pounds) = 50 * (100 + additional pounds) [multiplying both sides by 100 to eliminate the fractions]
3000 + 30 * additional pounds = 5000 + 50 * additional pounds [multiplying both sides]
50 * additional pounds - 30 * additional pounds = 5000 - 3000 [rearranging terms]
20 * additional pounds = 2000
additional pounds = 2000 / 20 = 100
Based on the calculation, you would need to add 100 pounds of copper and 100 pounds of iron to obtain an alloy containing 30% copper and 50% iron.