Question

The sum of three numbers is `120`. If the first number is `(2x - 15)` and the second is `(x - 3)` what expression can represent the third? and solve for all three numbers.

Answer 1

`"third number" = 138-3x`

Explanation:

The missing number will be the difference between the total and the sum of the other two numbers:

`"third number" = 120-((2x-15)+(x-3))`

`= 120-(3x-18)`

`= 120-3x+18`

`=138-3x`

There is not enough information to solve for a specific third number. It will depend on the value of `x`

Answer 2

`5,7" and 108 are possible"`

Explanation:

`"let the third number "=y`

`rArr2x-15+x-3+y=120`

`rArr3x-18+y=120`

`"subtract "3x-18" from both sides"`

`rArry=120-3x+18=138-3x`

`rArr"third number "=138-3x`

`"the sum of the first 2 numbers "=120-" third number"`

`rArr3x-18=120-(138-3x)`

`rArr3x-18=3x-18larrcolor(blue)"both sides are equal"`

`rArr"there are an infinite number of solutions"`

`"any value of x will generate the 3 terms"`

`color(blue)"For example"`

`x=10" then"`

`2x-15=20-15=5`

`x-3=10-3=7`

`138-30=108`

`"and "5+7+108=120`

`rArr5,7,120larrcolor(blue)"possible 3 numbers"`

`x=-1" then"`

`2x-15=-2-15=-17`

`x-3=-1-3=-4`

`138-3x=138+3=141`

`"and "-17+(-4)+141=120`

`rArr-17,-4,141larrcolor(blue)"possible 3 numbers"`