Final answer:
To find the mass of each alloy needed to create a 60 kg alloy of 51% copper, set up two equations based on the masses and percentages of copper and solve for 'x' and 'y'. However, more information is needed to determine how to create a 40% copper alloy. The total weight of the combined alloys will be 60 kg.
Step-by-step explanation:
To solve the problem of creating a 60 kg alloy of 51% copper using two alloys with different copper contents, we can set up a system of linear equations. Let's define 'x' as the mass of the 30% copper alloy and 'y' as the mass of the 65% copper alloy needed.
The first equation comes from the total mass of the alloy: x + y = 60 (since the total mass needed is 60 kg).
The second equation is derived from the copper percentages:
0.30x + 0.65y = 0.51×60 (representing the total mass of copper in the final alloy).
We can solve this system by substitution or elimination. Once we solve for 'x' and 'y,' we have the answer to parts (a) and (b).
As for (c), the student has not provided enough information to create a desired 40% copper alloy from the two given alloys.
Regarding part (d), the total weight of the combined alloys is the sum of the two alloy masses used, which, according to the information given, should be 60 kg as this is the target mass for the new alloy.