Question

There are two numbers twice as far from 14 as they are from 20 what are the numbers?

Answer 1

(abs(x-14))=2abs(x-20) square each side to get away from absolute value .
(x-14)^2=4*(x-20)^2
multiply those out, gather terms, and you get
x^2-44x+468=0 which factors to
(x-27)(x-17)=0 and you have the two numbers.

Answer 2

|x-14| = 2|x-20|
Clearly x cannot be less than 14, since it will then be closer to 14 than to 20
So, if 14 < x < 20 we have x-20 < 0, so
x-14 = 2(20-x)
x = 18
18 is 4 away from 14 and 2 away from 20

Or, note that since 20 is 6 away from 14, x will be 2/3 of the way from 14 to 20, or 4 away from 14.

The final choice is x > 20, so
x-14 = 2(x-20)
solve that for x.

Or, note that 20 is 6 away from 14, so move away another 6 from 20, and you find that
26 is 12 away from 14 and 6 away from 20.

Answer 3

17*27 cannot be 468, or any even number!

Answer 4

it's 18 and 20 because it is twice as far from 14 as they are from 20.

Answer 5

There are two numbers twice as far as 2 as they are far from 14. One number is 10. What is the other number?

Answer 6

18 and 26