pure tin was mixed with a4%in tin alloy to produce an ally that was 16%tin .How much pure in and how much 4% alloy were used to produce 32 kg of 16% alloy ?

Accepted Solution

Answer:4 kg of pure tinStep-by-step explanation:Let x kg be the amount of pure tin and y kg be the amount of 4% tin alloy mixed. 1. The weight of the mixture is 32 kg, then [tex]x+y=32[/tex]2. There are 4% of tin in y kg of 4% tin alloy, so there are [tex]0.04y[/tex] kg of tin in this alloy. There are 16% of tin in 32 kg of the mixture, then there are [tex]0.16\cdot 32=5.12[/tex] kg of tin in alloy. Thus,[tex]x+0.04y=5.12[/tex]3. Solve the system of two equations:[tex]\left\{\begin{array}{l}x+y=32\\x+0.04y=5.12\end{array}\right.[/tex]From the first equation[tex]x=32-y[/tex]Substitute it into the second equation:[tex]32-y+0.04y=5.12\\ \\3,200-100y+4y=512\\ \\-100y+4y=512-3,200\\ \\-96y=-2,688\\ \\y=28\\ \\x=32-28=4[/tex]