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.

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- Dec 6th 2008, 07:00 AMmagentaritaFind 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.

- Dec 6th 2008, 07:24 AMMoo
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.

Quote:

The largest increased by 2 equals twice the result of diminishing the middle number by 2.

Solve the system :

$\displaystyle \left\{\begin{array}{lll} x=y+z \\ x=3z+2 \\ x=2y-6 \end{array} \right.$ - Dec 7th 2008, 09:06 AMmagentaritaok...