Fake gold bricks are made by covering concrete cubes with gold paint, so the cost of the paint is proportional to their surface area while the cost of the concrete is proportional to their volume. If a 1 inch cube costs $1.30 to make while a 2 inch cube costs $6.80, then how much would a 3 inch cube cost?
Let P = the amount of money required to paint 1 square inch of a cube
Let C = the amount of money required to pour 1 cubic inch of concrete
1st equation: for a one inch cube C + 6P = 1.30 a 1" cube holds 1 in^3 and has 6 sides 1"x1" each
2nd equation: for a two inch cube 8C + 24P = 6.80 a 2" cube holds 8 in^3 and has 6 sides 2"x2" each
8C + 48P = 10.40 multiplied every term of 1st equation by 8
24P = 3.60 subtracted 2nd equation from the above to eliminate 8C
P = 0.15 divided both sides by 24
substitute 0.15 for P in 1st equation C + (6)(0.15) = 1.30
C + 0.90 = 1.30
subtract 0.90 from both sides C = 0.40
A 3" cube holds 27 in^3 and has 6 sides 3"x3" each
The cost will be 27C + 54P = (27)(0.40) + (54)(0.15) = 10.80 + 8.10 = 18.90 dollars
