A metalworker has a metal alloy that is 30% copper and another alloy that is 55% copper. How many kilograms of each alloy should the metalworker combine to create 80kg of a 45% copper alloy?
Answer:
32 kg of 30% copper
48 kg of 55% copper
Step-by-step explanation:
Let x represent the mass of 55% copper alloy that is to be used in the mix. Then 80-x is the mass of 30% copper alloy to be used. The total amount of copper in the mix is then ...
... 0.55x + 0.30(80-x) = 0.45·80
... 0.25x = 12 . . . . . . simplify, subtract 24
... x = 48 . . . . . . . . . divide by the coefficient of x
... 80-x = 32 . . . . . . the mass of 30% copper alloy required
The metalworker should combine 32 kg of 30% copper alloy with 48 kg of 55% copper alloy to make 80 kg of 45% copper alloy.
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I borrowed it......
To solve this problem, we will use a system of equations. Let's call the amount of the 30% copper alloy x (in kg) and the amount of the 55% copper alloy y (in kg).
We know that the total amount of the new alloy is 80 kg, so we have the equation:
x + y = 80
We also know that the amount of copper in the final alloy is 45% of 80 kg (0.45 * 80 = 36 kg):
0.30x + 0.55y = 36
Now we have a system of two equations, and we can solve it using substitution or elimination.
Let's solve it using substitution:
Rearrange the first equation to solve for x:
x = 80 - y
Now substitute this value of x into the second equation:
0.30(80 - y) + 0.55y = 36
Distribute the 0.30:
24 - 0.30y + 0.55y = 36
Combine like terms:
0.25y + 24 = 36
Subtract 24 from both sides:
0.25y = 12
Divide both sides by 0.25 to isolate y:
y = 12 / 0.25 = 48
Now substitute the value of y back into the first equation to find x:
x + 48 = 80
x = 80 - 48 = 32
So, the metalworker should combine 32 kg of the 30% copper alloy and 48 kg of the 55% copper alloy to create 80 kg of a 45% copper alloy.