Question

The sum of the ages of a father and son is 50years.five years ago the product of their ages are 175 . Find their present ages

Answer 1

Answer:

The father's present age is 46 years and the son's present age is 4 years.

Step-by-step explanation:

It is provided that the sum of the ages of a father and son is 50 years.

Let the son's age be y years and father's age be x years.

Then according to the condition provided: x + y = 50...(i)

Also it is provided that the product of their ages is 175.

That is, x × y = 175.

The expansion of (a + b)² is a² + 2ab + b².

And the expansion of (a - b)² is a² - 2ab + b².

Use the expansion of (a + b)² to determine the value of (x² + y²) as follows:

$(x+y)^{2}=x^{2}+y^{2}+2xy\\(50)^{2}=x^{2}+y^{2}+(2\times175)\\x^{2}+y^{2}=2500-350\\=2150$

Now determine the value of (x - y) using the expansion of (a - b)² as follows:

$(x-y)^{2}=x^{2}+y^[2}-2xy\\=2150-(2\times175)\\=1800\\(x-y)=\sqrt{1800} \\=42.426\\\approx42$

Now solve x + y = 50 and x - y = 42 simultaneously:

$x + y = 50\\x - y = 42\\\_\_\_\_\_\_\_\_\_\_\_\_\_\\\2x=92\\x=46$

Substitute x = 46 in x + y = 50 and solve for y as follows:

$x + y = 50\\46+y=50\\y=4$

Thus, the father's present age is 46 years and the son's present age is 4 years.