In the previous post, we have used quadratic equations to solve a word problem involving consecutive numbers. In this post, we discuss more quadratic problems. This is the second problem in the series.
Miel is 12 years older than Nina. The product of their ages is 540.
Let x = age of Nina
x + 12 = age of Miel
The product of their ages is 540, so we can multiply the expressions above and equate the product to 540. That is,
x(x + 12) = 540.
Multiplying the expressions, we have
Subtracting 540 from both sides, we obtain
We want to find two numbers whose product is -540 and whose sum is 12. Those numbers are -18 and 30.
This means that the factors are
(x – 18)(x + 30) = 0.
Equating each expression to 0, we have
x – 18 = 0, x = 18
x + 30 = 0, x = – 30.
Since we are talking about age, we take the positive answer x = 18.
This means that Nina is 18 years old. Therefore, Miel is 18 + 12 = 30 years old.