The difference of two numbers is 20 and their product is 125, what is the answer?

find prime factors to get the inbetween numbers for product, and choose the one that has a difference of 20, and it should be 5 and 25, both requirements are met.

Solution 1: The numbers are 25 and 5

Solution 2: The numbers are -5 and -25

Step-by-step explanation:

We have 2 unknown numbers, then we can define them as:

x: Unknown number 1  

y: Unknown number 2

The problem states that "the difference of two numbers is 20". We can translate this to x - y = 20

We also know that "their product is 125". We can translate this to x . y = 125

Putting both equations together, we get the following system of equations

Now, to solve this system of equations we can use the Substitution Method.

We can solve 1st equation for x, by adding y to both sides

x - y + y = 20 + y

x = 20 + y

We can substitute x by 20 + y on the 2nd equation

(20 + y) . y = 125

Applying distributive property on the left side

20y + y² = 125

Substracting 125 to both sides and rearranging the terms, we get

20y + y² - 125 = 125 -125

y² + 20y - 125 = 0

We can apply the quadratic equation attached to solve this (with a = 1, b = 20, c = -125).

( -20 ± √(20² - 4 . 1 . -125) ) / ( 2. 1 ) =

( -20 ± √(400 + 500) ) / ( 2) =

( -20 ± √900 ) / ( 2) =

( -20 ± 30 ) / ( 2) =

We get 2 results:

For each of these values of y, we can find the corresponding value of x:

the barter

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.