What are my numbers?

Question

I am thinking of two numbers.

When I add my numbers, the answer is 1

When I multiply my numbers, the answer is 0.09

 

What are my numbers?

Answer 1

Hi Marie,

 

Good job with the application of system equations. Your answer is 0.1, 0.9. 

 

Here is how I got these two numbers:

Let one number = X, another number = Y.

X + Y =1----(1)

XY= 0.09----(2)

 

(1): X = 1-Y

Plug into (2):(1-Y)Y = 0.09

Y-Y²-0.09 = 0

Y²-Y+0.09 = 0

Y=(1±√1-0.36)/2 (quadratic formula)

Y = (1±0.8)2

Y=0.9 or Y =0.1

Plug into X+Y =1:

X=0.1 or X=0.9

 

 

 

Answer 2

2 equations in 2 unknowns

x+y = 1 --> EQ1

xy = 0.09 --> EQ2

 

from equation 2

x=0.09/y

 

substitute in EQ1

0.09/y + y = 1

multiply all sides by y 

y² - y + 0.09 = 0

(y-0.9)(y-0.1) = 0

y= 0.9 or 0.1

and

x = 0.1 or 0.9