March 2022
Problem of the Month

Number Problem

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

Send any comments or questions to: David Pleacher