Question

The cost of making a table partly varies as the area and partly varies as square of the length. lf the cost of a table 2m by 3m is $50000 and the cost of a table 1.5m by 4m is $64000. Find the cost of a table 2m by 4m.

Answer 1

Let's assume that the cost of the table is directly proportional to the area and the square of the length. Therefore, we can write the equation:

Cost = k * (Area) * (Length^2)

where k is the constant of proportionality.

From the given information, we have two equations:

1) Cost1 = k * (Area1) * (Length1^2)
$50000 = k * (2m * 3m) * (2m^2)

2) Cost2 = k * (Area2) * (Length2^2)
$64000 = k * (1.5m * 4m) * (4m^2)

Let's divide equation 2 by equation 1 to eliminate k:

Cost2/Cost1 = (Area2 * Length2^2) / (Area1 * Length1^2)
($64000/$50000) = ((1.5m * 4m) * (4m^2)) / ((2m * 3m) * (2m^2))

Simplifying this expression:

1.28 = (6m^3) / (6m^3)

So, the value of 1.28 holds true for the ratio of the costs of two tables. Let's assume the cost of the table 2m by 4m is C:

C = 1.28 * Cost1
C = 1.28 * $50000
C = $64000

Therefore, the cost of a table 2m by 4m is $64000.