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.
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.
Answer:
Let’s denote the ages of the two friends as A and B. According to the information given:
- The sum of their ages is 20: A + B = 20
- Four years ago, the product of their ages was 48: (A - 4) * (B - 4) = 48
Now, we can solve these two equations simultaneously to find their present ages.
From the first equation, we have A = 20 - B.
Substitute this value of A into the second equation to solve for B:
(20 - B - 4) * (B - 4) = 48
(16 - B) * (B - 4) = 48
-B^2 + 20B - 64 = 48
-B^2 + 20B - 112 = 0
B^2 - 20B + 112 = 0
Now, solve this quadratic equation to find the possible ages of the friends. We can use the quadratic formula:
B = (-(-20) ± √((-20)^2 - 41112)) / 2*1
B = (20 ± √(400 - 448)) / 2
B = (20 ± √(-48)) / 2
As the square root of a negative number is not real, it means that there are no real solutions.
Therefore, the initial situation provided is not possible with real numbers.