Question

The cost of a square slab is proportional to its thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 meters long and 0.1 meter thick?
(1) The cost of a square slab that is 2 meters long and 0.2 meter thick is $160 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.

(2) The cost of a square slab that is 3 meters long and 0.1 meter thick is $200 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.

Answer 1

Answer:

$520

Explanation:

Using information provided in the question, equations can be formed to determine the unknown proportionality factors.

$C=AT + BL^2$ , where C is the cost, T is the thickness, L is the length and A and B are the proportionality factors

Equation 1:

Slab 1: $C_1=0.2A + 2^2B=0.2A+4B$

Slab 2: $C_2=0.1A + 2^2B=0.1A+4B$

$C_1=C_2+160$

$0.2A+4B=0.1A+4B+160$

$0.1A=160$

$A=1600$

Equation 2:

Slab 2: $C_2=0.1A + 3^2B=0.1A+9B$

Slab 3: $C_3=0.1A + 2^2B=0.1A+4B$

$C_2=C_3+200$

$0.1A+9B=0.1A+4B+200$

$5B=200$

$B=40$

After determining unknowns A=1600 and B=40, these can be substituted into $C=AT + BL^2$ to give below

$C=1600T + 40L^2$

Cost is to be determined for T=0.1m and L=3m

$C=1600T + 40L^2$

$C=1600(0.1) + 40(3)^2$

$C=160 + 360$

$C=520$

The cost of a square slab of 3 meter length and 0.1 meter thickness is $520

Answer 2

Answer:

(1) The cost of the square slab is $360

(2) The cost of the square slab is $360

Explanation:

Cost (C) varies as thickness (t) and square of length (L^2)

Therefore, C = ktL^2

Case 1

C1 = 160 + C2

C1 - C2 = 160

C1 = ktL^2 (t = 0.2, L = 2)

C1 = k×0.2×2^2 = 0.8k

C2 = ktL^2 (t = 0.1, L = 2)

C2 = k×0.1×2^2 = 0.4k

C1 - C2 = 0.8k - 0.4k = 0.4k

C1 - C2 = 0.4k

160 = 0.4k

k = 160/0.4 = 400

C = ktL^2 (t = 0.1, t = 3)

C = 400×0.1×3^2 = $360

Case 2

C1 = 200 + C2

C1 - C2 = 200

C1 = ktL^2 (t = 0.1, L = 3)

C1 = k×0.1×3^2 = 0.9k

C2 = ktL^2 (t = 0.1, L = 2)

C2 = k×0.1×2^2 = 0.4k

C1 - C2 = 0.9k - 0.4k = 0.5k

C1 - C2 = 0.5k

200 = 0.5k

k = 200/0.5 = 400

C = ktL^2 (t = 0.1, L = 3)

C = 400×0.1×3^2 = $360