Question

A goldsmith combined an alloy that costs $4.40 per once with an alloy that costs $1.90 per ounce. How many ounces of each were used to make a mixture of 200 oz costing $2.40 per ounce? $4.40 alloy = how many oz? $1.90 alloy = how many oz?

Answer 1

Let:

x = oz of 4.40 alloy

y = oz of 1.90 alloy

`\begin{gathered} 4.4x+1.9y=2.4(200) \\ \end{gathered}`

Where:

y = 200 - x

so:

`\begin{gathered} 4.4x+1.9(200-x)=480 \\ 4.4x+380-1.9x=480 \end{gathered}`

Solve for x:

`\begin{gathered} 4.4x-1.9x=480-380 \\ 2.5x=100 \\ x=(100)/(2.5) \\ x=40oz \end{gathered}`

Replace x into y = 200 - x:

`\begin{gathered} y=200-40 \\ y=160oz \end{gathered}`

Answer:

40 oz of $4.40 alloy

160 oz of $1.90 alloy