# Find the Numbers

• December 6th 2008, 07:00 AM
magentarita
Find the Numbers
A number equals the sum of two other numbers. The largest number diminished by 2 equals three times the smallest. The largest increased by 2 equals twice the result of diminishing the middle number by 2. Find the numbers.

• December 6th 2008, 07:24 AM
Moo
Hello,

Suppose the numbers are positive.
Let x,y,z be the numbers with x>y>z.
Since they're positive, it is obvious that x=y+z.

Quote:

The largest number diminished by 2 equals three times the smallest.
x-2=3z ====> x=3z+2

Quote:

The largest increased by 2 equals twice the result of diminishing the middle number by 2.
x+2=2(y-2) ====> x=2y-6

Solve the system :

$\left\{\begin{array}{lll} x=y+z \\ x=3z+2 \\ x=2y-6 \end{array} \right.$
• December 7th 2008, 09:06 AM
magentarita
ok...
Quote:

Originally Posted by Moo
Hello,

Suppose the numbers are positive.
Let x,y,z be the numbers with x>y>z.
Since they're positive, it is obvious that x=y+z.

x-2=3z ====> x=3z+2

x+2=2(y-2) ====> x=2y-6

Solve the system :

$\left\{\begin{array}{lll} x=y+z \\ x=3z+2 \\ x=2y-6 \end{array} \right.$

This is a tricky one. Thanks.