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?
+128473 Let the cost of a square inch of paint = p
Let the cost of a cubic inch of concrete = c
The surface area (in square inches) of a 1 inch cube = 6(1)^2 = 6
The volume of 1 inch cube (in cubic inches) = 1^3 = 1
The surface area of a two inch cube = 6(2)^2 = 24
The volume of a 2 inch cube = 2^3 = 8
So.....we have this system of equations
6p + 1c = 1.30 ⇒ c = 1.30 - 6p (1)
24p + 8c = 6.80 (2)
Sub (1) into (2) and we have
24p + 8 ( 1.30 - 6p) = 6.80 simplify
24p + 10.4 - 48p = 6.80
-24p + 10. 4 = 6.80
-24p = -3.6 divide both sides by -24
p = .15
So c = 1.30 - 6(.15) = 1.30 - .90 = .40
So......a 3 inch cube has surface area of 6(3)^2 = 54 in^2
And the volume is (3)^3 = 27 in^3
So.....the cost of a 3 inch cube is
54(.15) +27(.40) = $18.90
