Can you show work por favor? :)
A metalworker has a metal alloy that is 20% copper and another alloy that is 60% copper. How many kilograms of each alloy should be combined to create 80 kg of a 53% copper alloy?
Ok, so you have x as the kg.
The equation should look like this:
.20(x) + .60(80-x) = .53(80)
Then you can multiply everything out to solve for x.
What is the factor (x to the third power + 4x to the second power)(2x+8)?
Certainly! To find out how many kilograms of each alloy should be combined, let's break down the problem step by step:
Let's assign variables for the unknowns:
Let x be the number of kilograms of the 20% copper alloy.
Let y be the number of kilograms of the 60% copper alloy.
Now, let's set up the equations:
1. Total mass equation:
The total mass of the alloy is 80 kg, so our equation for the total mass is:
x + y = 80
2. Copper content equation:
The copper content in the alloy is given as 53%. The copper content of x kg of the 20% copper alloy is 0.2x kg, and the copper content of y kg of the 60% copper alloy is 0.6y kg. The copper content equation is:
(0.2x + 0.6y) / 80 = 0.53
Now, we have a system of two equations with two unknowns:
x + y = 80
(0.2x + 0.6y) / 80 = 0.53
To solve this system, we can use either substitution or elimination method. Let's solve it by elimination:
First, multiply the second equation by 80 to get rid of the fraction:
0.2x + 0.6y = 80 * 0.53
This simplifies to:
0.2x + 0.6y = 42.4
Now, let's multiply the first equation by 0.2 to make the coefficients of x the same:
0.2x + 0.2y = 16
Now, subtract the second equation from the first equation:
(0.2x + 0.6y) - (0.2x + 0.2y) = 42.4 - 16
Simplifying further:
0.6y - 0.2y = 26.4
Combining like terms:
0.4y = 26.4
Now, solve for y by dividing both sides by 0.4:
y = 26.4 / 0.4
y = 66
Now that we have the value of y, substitute it back into the first equation to solve for x:
x + 66 = 80
x = 80 - 66
x = 14
Therefore, the metalworker should combine 14 kg of the 20% copper alloy and 66 kg of the 60% copper alloy to create 80 kg of a 53% copper alloy.