徵求新解法~~~~~~~

hijenny

214. 20789-!-item-!-187;#058&013258

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.

選D
算這題要算很久
有戰友知道快的解法嗎??

yzg1236

你是咋算的呢？

hijenny

根據這題意 :
因為是square, 所以long and width是一樣的.
1. a square slab is proportional to its thickness
假設thickness = T => T * k1
2. also proportional to the square of its length
假設length = L => L * k2
成本C = T * k1 * L^2 * k2^2
=> C = T * L^2 * (k1*k2^2) 由於不管length or thickness怎樣變動, 常數(constant)都不會變, 因為他是成比例的, 因此簡化為 (k1*k2^2) = K
=> T * L^2 * K

C=cost, k=constant, T=thickness, L =length
C= k * T * L^2

so when T=0.1, L=3, C=?
(we need to know the value of k)

(1) The cost of a square slab that is 2 meters long and 0.2 meter thick
--> C= k * 0.2 * 2^2
the cost of a square slab that is 2 meters long and 0.1 meter thick
--> C= k * 0.1 * 2^2
difference of two costs=160 (given)
--> (k * 0.2 * 2^2) - (k * 0.1 * 2^2) =160
so you can get the value of k=400 ---> sufficient
(2) The cost of a square slab that is 3 meters long and 0.1 meter thick
--> C= k * 0.1 * 3^2
the cost of a square slab that is 2 meters long and 0.1 meter thick
--> C= k * 0.1 * 2^2
difference of two costs=200 (given)
--> (k * 0.1 * 3^2) - (k * 0.1 * 2^2) =200
so you can get the value of k=400 ---> sufficient