Question

Among all pairs of numbers whose difference is 14 find a pair whose product is as small as possible

Answer 1

The pair two numbers whose difference is 14 and the product is as small as possible (i.e. -49) are (-7,7)

What are word problems?

In mathematical concepts, word problems involve a crucial understanding of the problem and knowing which mathematical method and arithmetic operations are best suited to solving the problem.

If we assume that the smaller number should be = a and the larger number = a + 14.

Thus, their product (X) can be expressed as:

= a(a+14)

= a² + 14a

The smallest possible value implies the minimum value, i.e.

$\mathbf{\dfrac{dX}{da} = 2a + 14}$

Thus,

2a + 14 = 0

a = - 14/2

a = -7

Therefore, we can conclude that the pair of two numbers whose difference is 14 and the product is as small as possible (i.e. -49) is (-7,7).

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