Question

A man is 5 years older than his wife the product of their ages is 750 find their ages

Answer 1

Let's represent the man's age as "x" and the wife's age as "y". We are given that the man is 5 years older than his wife, so we can write an equation:

x = y + 5

We are also given that the product of their ages is 750:

x * y = 750

Now we can substitute the value of x from the first equation into the second equation:

(y + 5) * y = 750

Expanding the equation:

y^2 + 5y = 750

Rearranging the equation to make it a quadratic equation:

y^2 + 5y - 750 = 0

Now we can factor this quadratic equation:

(y + 30)(y - 25) = 0

Setting each factor equal to zero:

y + 30 = 0 or y - 25 = 0

Solving for y:

y = -30 or y = 25

Since age cannot be negative, we can discard the solution y = -30. Therefore, the wife's age is 25.

Now we can substitute this value into the first equation to find the man's age:

x = y + 5
x = 25 + 5
x = 30

So, the husband is 30 years old and the wife is 25 years old.