Respuesta :
Let x be the pounds of 45% copper alloy
Let y be the pounds of 69% copper alloy
To get the amount of copper in a alloy you multiply the pounds of it by the % of copper in decimal form.
Use 0.45x and 0.69y to get a alloy of 42*0.66 (42 pounds containig 66% copper)
[tex]\begin{gathered} 0.45x+0.69y=42\cdot0.66 \\ \\ 0.45x+0.69y=27.72 \end{gathered}[/tex]x and y needs to sum the pounds in the last alloy:
[tex]x+y=42[/tex]Use the next system of equations to solve the given problem:
[tex]\begin{gathered} 0.45x+0.69y=27.72 \\ x+y=42 \end{gathered}[/tex]1. Solve y in the second equation:
[tex]y=42-x[/tex]2. Substitute the y in the first equation by the value you get in first step:
[tex]0.45x+0.69(42-x)=27.72[/tex]3. Solve x:
[tex]\begin{gathered} 0.45x+28.98-0.69x=27.72 \\ -0.24x+28.98=27.72 \\ -0.24x=27.72-28.98 \\ -0.24x=-1.26 \\ x=\frac{-1.26}{-0.24} \\ \\ x=5.25 \end{gathered}[/tex]4. Use the value of x to solve y:
[tex]\begin{gathered} y=42-x \\ y=42-5.25 \\ y=36.75 \end{gathered}[/tex]Solution: x=5.25, y=36.75
