Question

A metallurgist has one alloy containing 41 % copper and another containing 54 % copper. How many pounds of each alloy must he use to make 40 pounds of a third

alloy containing 45 % copper? (Round to two decimal places if necessary.)
Step 1 of 2: Use the variables x and y

Answer 1

30.39 and 10.26 pounds.

Explanation:

Step 1 of 2: if the variables x (for 41% alloy) and y (for 54% alloy), then

Step 1 of 2: it is possible to make up the system of two equations:

`\left \{ {{x+y=0.45*40} \atop {0.41x+0.54y=0.45(x+y)}} \right. < = > \ \left \{ {{y=(72)/(13) } \atop {x=(162)/(13)}} \right.`

then the mass of the alloy containing 41% of coper is 162/13:0.41≈30.39

the mass of the alloy containing 54% of copper is 72/13:0.54=10.26.