Question

I need help on finding a sum of 2 numbers that adds up to 186. The difference between them is 32, can you help me?

Answer 1

77 and 109

Explanation:

With two unknowns it is necessary to have two equations.

Let x = one number
Let y = the other number

`x + y = 186`
`x-y = 32`

Solve the second equation for x

`x - y + y = 32 + y` This gives a value for x

`x = 32 + y` Put this value into the first equation

`32 + y + y = 186` Solve this equation for y

`32 + 2y = 186` subtract 32 from both sides

`32- 32 + 2y = 186 - 32` this gives

`2y = 154` divide both sides by 2

# 2y /2 = 154/2 so

`y = 77`

Put this value in for the second equation for x

`x = 77 + 32`

`x = 109`

Answer 2

`x = 109`

`y = 77`

General steps are in bold.

Explanation:

Make two equations. Let `x` represent the first number and `y` represent the second number.

First equation: The sum of two numbers adds up to `186`:

`color(red)(x + y = 186)`

Second equation: The difference between the two numbers is `32`:

`color(green)(x - y = 32)`

Now you can solve for one of the variables by taking either equation. I will use the first equation to solve for `x`.

`color(red)(x + y = 186)`

`color(white)(.....)color(orange)(x = 186 - y)`

Since you now know what `x` is equal to, you can sub it into the second equation then solve for `y`.

`color(white)(............)color(green)(x - y = 32)`

sub in `color(orange)(x = 186 - y)`

`(color(orange)(186 - y)) - y = 32`

`color(white)(.......)186 - 2y = 32`

`color(white)(.............)-2y = 32 - 186`

`color(white)(.............)-2y = - 154`

`color(white)(...................)y = 77`

Now you have the `y` value. You can sub this into either equation to find the `x` value. I will use the first equation.

`color(white)(.)color(red)(x + y = 186)`

sub in `y = 77`

`x + 77 = 186`

`color(white)(........)x = 109`

Therefore the two numbers are `109` and `77`.