Question

4. Is the following situation possible? If so, determine their present ages.
The sum of the ages of two friends is 20 years. Four years ago, the product of their ages
in years was 48.
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Answer 1

Answer:

Yes. It is possible.

Step-by-step explanation:

Let the age of one friend be x years.

Then, age of the other friend = (30 - x) years.

Four Years Ago,

Age of friend whose present age is x years = (x-4) years

And, Age of friend whose present age is (30 - x) years = (30 - x - 4) = (26 - x) years.

According the question,

$(x-4)(26-x) = 48\\\\\implies 26x - x^2 - 104 + 4x = 48\\\\\implies -x^2 + 30x - 104 - 48 = 0\\\\\implies -x^2 + 30x - 152 = 0\\\\\implies x^2 - 30x + 152 = 0$

Here, a = 1

         b = -30

         c = 152

And, D = b² - 4ac

= (-30)² - 4(1)(152)

= 900 - 608

= 292

Since, D is positive, the situation is possible.