An alloy of metals is 25% copper .Another alloy is 50% copper. How much of each alloy should be used to make 1000grams of an alloy that is 45% copper?
.25(x)+.50(1000-x)=.45(1000)
where x is the number of grams of 25% copper
and 1000-x is the rest of the 1000 grams i.e. the number of grams of 50%
To solve this problem, we can set up a system of equations. Let's call the amount (in grams) of the first alloy as "x" and the amount of the second alloy as "y".
Since the first alloy is 25% copper, the amount of copper in it can be calculated as 0.25x. Similarly, the amount of copper in the second alloy is 0.50y.
We want to create a final alloy that is 45% copper by combining the two alloys. The total amount of copper in the final alloy can be calculated as 0.45 * 1000 grams (since it is given that we want to make 1000 grams of the final alloy).
Now, we can set up the equation:
0.25x + 0.50y = 0.45 * 1000
Simplifying the equation:
0.25x + 0.50y = 450
We also know that the total amount of alloy used is 1000 grams, so we can set up another equation:
x + y = 1000
Now, we have a system of equations:
0.25x + 0.50y = 450
x + y = 1000
To solve this system, we can use substitution or elimination method. Let's use the elimination method:
Multiply the second equation by 0.25 to make the x coefficients equal:
0.25x + 0.25y = 250
Now, subtract the above equation from the first equation to eliminate x:
0.25x + 0.50y - (0.25x + 0.25y) = 450 - 250
0.25x + 0.50y - 0.25x - 0.25y = 200
0.25y = 200
Divide both sides of the equation by 0.25:
y = 800
Now, substitute this value of y back into one of the original equations:
x + y = 1000
x + 800 = 1000
x = 200
Therefore, to make 1000 grams of an alloy that is 45% copper, we should use 200 grams of the 25% copper alloy and 800 grams of the 50% copper alloy.