Question

Question #95196

Answer 1

Larger number is `37` and smaller number is `26`

Explanation:

Suppose the smaller number is `x`
and, the larger number is `x+11`

Now, its given that: `x+11` + `5x` = `167`.....(1)

Solving for `x`, Equation (1) can be written as:

`6x+11` = `167`

or, `6x` = `167-11` = `156`

or, `x` = `cancel156^26/cancel6^1` = `26`

Therfore, the larger number will be `x+11` = `26+11` = `37`

Answer 2

`37" and "26`

Explanation:

`"let the smaller number "=x`

`"then the larger number "=x+11`

`rArrx+11+5x=167larrcolor(blue)"solve for x"`

`rArr6x+11=167`

`"subtract 11 from both sides"`

`6xcancel(+11)cancel(-11)=167-11`

`rArr6x=156`

`"divide both sides by 6"`

`(cancel(6) x)/cancel(6)=156/6`

`rArrx=26`

`"smaller number "=x=26`

`"larger number "=x+11=26+11=37`

`color(blue)"As a check"`

`37+(5xx26)=37+130=167larr"True"`