PETS/SAT (0006)

来源：百度知道 编辑：UC知道 时间：2024/05/24 13:20:28
PETS/SAT (0006) 要过程，要步骤

Mrs.Lee gave birth to 4 children in 4 consecutive years.
Today, she discovered that the poduct of the ages, in years, of her 4 children is 24024.
How old are her children now ?

Solution:let the 4 childs are (x-0.5)、(x+0.5)、(x-1.5)、(x+1.5)

Equate:(x-0.5)(x+1.5))(x-1.5)(x+0.5)=24024
∴（x²+x-0.75)（x²+x-0.75)=24024
∴【（x²-0.75）+x】【（x²-0.75）-x】=24024
（x²-0.75）²-x²=24024

And then，let y=x²
∴y²--0.5y+0.5625=24024
(y-0.25)²+0.5=24024
∴x≈12.5
so the 4 childs ages are 11、12、13、14.

可以用英文解释么？

The question is basically asking ：
The product of four consecutive numbers is 24024, what are these numbers？

First, because 24024 ends with a 4, the four consecutive numbers end with either：

1, 2, 3, 4

OR

6, 7, 8, 9

I reached this conclusion because all other combination of four consecutive numbers multiplied together will give you a product that ends with 0 instead of a 4.

Next, I will narrow down the parameters. All four of her children must be under 20, because 20^4 = 160,0