Zandile is 4 years older than Thoko.Four years ago the product of their ages was 165.find their present ages
thoko ---x
zandile -- x+4
4 years ago:
thoko -- x-4
zandile -- x
x(x-4) = 165
x^2 - 4x - 165 = 0
(x-15)(x+11)
x = 15 or x = -11
state the conclusion
To find Zandile and Thoko's present ages, we'll need to set up equations based on the given information.
Let's assume that Thoko's present age is x years. Since Zandile is 4 years older than Thoko, Zandile's present age can be expressed as (x + 4) years.
Four years ago, Thoko's age would have been (x - 4) years, and Zandile's age would have been (x + 4 - 4) = (x) years. Given that their ages multiplied together equals 165, we can write the equation:
(x - 4) * (x) = 165
Expanding this equation, we get:
x^2 - 4x = 165
Rearranging the equation to put it in standard quadratic form:
x^2 - 4x - 165 = 0
Now, we can solve this quadratic equation to find the value of x.
Using factoring method or quadratic formula, we find that x = 15 or x = -11. However, we can eliminate the negative value because we are considering ages, which cannot be negative.
Therefore, Thoko's present age (x) is 15 years.
Now, we can find Zandile's present age by substituting x = 15 into the expression we derived earlier:
Zandile's age = x + 4 = 15 + 4 = 19 years
So, Thoko is currently 15 years old, and Zandile is currently 19 years old.