How do I set up this word problem

Question

The coins are to be made from an alloy that is 40% silver. The foundry has on hand two alloy, one with 50% silver content and one with 25% silver content. How many kilograms of each alloy should be used to make 20 kilograms of the 40% silver alloy.

Answer 1

The equations are:

0.5 X + 0.25Y = 0.40 *20

X + Y = 20

then we obtain

X = 20 - Y

replacing in the first equation we have:

0.5(20-Y) + 0.25Y = 8

10 - 0.5y + 0.25Y = 8

solving for Y; Y = 8 Kg

Then x= 12 Kg

being X = the alloy with 50% silver

Y the one with 24% silver

 

 

 

Answer 2

Let x = the number of kg of the 50% alloy.  The number of kg of the 25% alloy is thus (20-x).

 

0.5x + 0.25(20-x) = 0.4(20 kg)

 

0.5x + 5 - 0.25x = 8 kg

 

0.25x = 3 kg

 

Solve for x