Question

Suma a 3 numere naturale este 163. Scazand al treilea numar din suma primelor doua numere, obtinem 67. Scazand primul numar din suma ultimelor 2 numere, obtinem 37. Determinati cele 3 numere

Answer 1

Answer: x=63, y=52, z=48

Explanation:

The complete question in english is:

The sum of 3 natural numbers is 163. By subtracting the third number from the sum of the first two numbers, we get 67. By subtracting the first number from the sum of the last 2 numbers, we get 37. Determine the 3 numbers

According to this we have a system with three equations and three unknown values:

`x+y+z=163` (1)

`x+y-z=67` (2)

`-x+y+z=37` (3)

Let's begin by isolating
`x` from (1):

`x=163-y-z` (4)

And substitute (4) in (2):

`163-y-z+y-z=67` (5)

Isolating
`z`:

`z=48` (6) We have found the first number

Substituting (6) in (1):

`x+y+48=163` (7)

Adding (7) to (3):

`\left \{ {{x+y+48=163} \atop {-x+y+z=37}} \right`

We have the following:

`2y+96=200`

Isolating
`y`:

`y=52` (8) This is the second number

Substituting (6) and (8) in (1):

`x+52+48=163` (9)

Isolating
`x`:

`x=63` (10) This is the third number