There are two numbers twice as far from 14 as they are from 20 what are the numbers?
|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.
18 and 26
17*27 cannot be 468, or any even number!
To find the two numbers that are twice as far from 14 as they are from 20, let's break down the problem step by step:
Step 1: Determine the distance between each number and 14.
Let's call the first number "x." The distance between x and 14 is given by the equation: |x - 14|. Similarly, the distance between the second number, let's call it "y," and 14 is given by the equation: |y - 14|.
Step 2: Determine the distance between each number and 20.
The distance between x and 20 is given by the equation: |x - 20|. The distance between y and 20 is given by: |y - 20|.
Step 3: Create the equation using the given information.
According to the problem, both numbers should be twice as far from 14 as they are from 20. Mathematically, this can be written as:
|x - 14| = 2 * |x - 20|
|y - 14| = 2 * |y - 20|
Step 4: Solve the equations simultaneously.
By solving the two equations, we can find the values of x and y. Let's solve the first equation:
|x - 14| = 2 * |x - 20|
For x < 20:
x - 14 = 2 * (x - 20)
x - 14 = 2x - 40
26 = x
For x > 20:
14 - x = 2 * (x - 20)
14 - x = 2x - 40
3x = 54
x = 18
So, we have two possible values for x: 26 and 18.
Similarly, we solve the second equation:
|y - 14| = 2 * |y - 20|
For y < 20:
y - 14 = 2 * (y - 20)
y - 14 = 2y - 40
26 = y
For y > 20:
14 - y = 2 * (y - 20)
14 - y = 2y - 40
3y = 54
y = 18
Again, we have two possible values for y: 26 and 18.
Hence, the two numbers that are twice as far from 14 as they are from 20 are 26 and 18.
it's 18 and 20 because it is twice as far from 14 as they are from 20.
There are two numbers twice as far as 2 as they are far from 14. One number is 10. What is the other number?
(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.