Problem: Finding the length of a table when the reading on a scale at one end is 4.0 cm and at the other end is 44.3 cm.

Solution:

To find the length of the table, we need to use the concept of proportionality. Let the length of the table be 'L'. Then, we can set up a proportion as follows:

4.0 cm / L = 44.3 cm / L + 40.3 cm

Simplifying this proportion, we get:

4.0 cm / L = 1 / (L/44.3 + 1)

Cross-multiplying and simplifying further, we get:

L^2 - 44.3L - 177.2 = 0

Solving this quadratic equation, we get:

L = 48.1 cm (approx.)

Therefore, the length of the table is approximately 48.1 cm.

Explanation:

The problem involves finding the length of a table when the readings on a scale at its two ends are given. To solve this problem, we need to use the concept of proportionality, which states that two quantities are proportional if they have a constant ratio. In this case, the ratio of the distances from the two ends of the table to their respective readings on the scale is constant, and therefore, we can set up a proportion.

We can simplify the proportion by cross-multiplying and rearranging the terms. This gives us a quadratic equation, which we can solve by using the quadratic formula. The positive root of the equation gives us the length of the table.

In conclusion, by using the concept of proportionality and solving a quadratic equation, we can find the length of the table when the readings on a scale at its two ends are given.

I think 40.3 cm