Let x and y are the per kg cost of firing clay and polymer clay.
5kg of firing clay and 24kg of polymer clay at a cost of $64.05,
5x+24y = 64.05....(1)
25kg of firing clay and 8kg of polymer clay at a cost of $51.45
25x+8y = 51.45 ......(2)
By multiplying equation 1 with 5
25x+120y = 320.25......(3)
Subtracting equation 2 from equation 3,
25x+120y -25x-8y = 320.25-51.45
112y = 268.80
y = 268.8/112
y = 2.4
Putting the value of y in equation 2,
25x+8×2.4 = 51.45
25x + 19.2 = 51.45
25x = 51.45-19.2
25x = 32.25
x = 32.25/25
x = 1.29
So cost of firing clay = $1.29 per kg
Cost of polymer clay = $2.4 per kg