What two numbers will give you an answer of 10 when one is subtracted from the other and an answer of 2000 when they are multiplied together?

Show your work (use algebra).



Solution to the Problem:


The numbers are 50 and 40, but also -40 and -50.

Let x = first number and let y = second number.

Then set up two equations:
x - y = 10
xy = 2000

From the second equation, we get x = 2000/y.

Substituting that value in the first equation gives   2000/y - y = 10

2000 - y2 = 10y
- y2 + 2000 - 10y = 0
y2 + 10y - 2000 = 0
(y - 40) (y + 50) = 0
So, y = 40 or y = -50.

So the answers that work would be:
x = 50 and y = 40   or   x = -40 and y = -50.


Correctly solved by:

1. Davit Banana Istanbul, Turkey
2. Mohamed Sheriff Freetown, Western area, Sierra Leone, West Africa
3. Ritwik Chaudhuri Santiniketan, West Bengal, India
4. Dr. Hari Kishan D.N. College,
Meerut, Uttar Pradesh, India
5. Veena Mg Bangalore, Karnataka, India
6. Sara Gagler Central High School,
Grand Junction, Colorado
7. Colin (Yowie) Bowey Beechworth, Victoria, Australia
8. Ivy Joseph Pune, Maharashtra, India