Question

The sum of two numbers is 4. Twice the larger is 11 more than the smaller. How do you find the smaller number?

Answer 1

The smaller number is `-1`.

Explanation:

Considering the two numbers as `x` and `y` where `x` is the larger number, we can write:

`x+y=4`
`2x=y+11`

From the first equation, we can determine a value for `x`.

`x+y=4`

Subtract `y` from both sides.

`x=4-y`

In the second equation, substitute `x` with `color(red)((4-y))`.

`2x=y+11`

`2color(red)((4-y))=y+11`

Open the brackets and simplify. The product of a positive and a negative is a negative.

`8-2y=y+11`

Add `2y` to both sides.

`8=3y+11`

Subtract `11` from both sides.

`-3=3y`

Divide both sides by `3`.

`-1=y` or `y=-1`

In the first equation, substitute `y` with `color(blue)(-1)`.

`x+y=4`

`x+(color(blue)(-1))=4`

Open the brackets and simplify. The product of a positive and a negative is a negative.

`x-1=4`

Add `1` to both sides.

`x=5`