Question

The cost C of sinking a wall x metres deep varies partly as x and partly as x2 A well of this#5000.00,if the depth is 30 m and cost is#8000.00 if the depth is 50m
derive an equation that connects C and x together.
how deep is the well if the cost is#12000.00.

Answer 1

C = kx + mx^2

when x = 30,
30k + 900m^2 = 5000 ---> 3k + 90m = 500 , #1
when x = 50
50k + 2500m = 8000 ---> 5k + 250m = 800 , #2

5 times #1 ---> 15k + 450m = 2500
3 times #2 ---> 15k + 750m = 2400
subtract them:
300m = -100
m = -1/3
sub into #1

3k + 90(-1/3) = 500
3k = 530
k = 530/3

C = (530/3)x - (1/3)x^2

so (530/3)x - (1/3)x^2 = 12000
530x - x^2 = 36000
x^2 - 530x + 36000 = 0

I will let you do some of the work, this quadratic solves nicely.