Question

Thirty two is the sum of a number and fifty one. What is the number?

Answer 1

The number is `-19`.

Explanation:

Let's call the unknown number `x` and set up an equation:
`x+51 =32`.

To solve for `x`, we want to get it alone. In this case, that means subtracting `51` from both sides:
`x = -19`

To check this, we go back to what we know: the sum is the result of addition, and if we add `-19 + 51`, we do indeed get `32`.

Answer 2

The number is `-19`.

Explanation:

Translate the sentence from English to math. For example, "is" means equals and "sum" means adding together numbers.

`stackrel(32) overbrace("Thirty two") " " stackrel(=) overbrace("is") " " stackrel(x+51) overbrace("the sum of a number and fifty one") "."`

Now, write down the equation and solve for `x`:

`32=x+51`

`32color(blue)-color(blue)51=x+51color(blue)-color(blue)51`

`32color(blue)-color(blue)51=xcolor(red)cancel(color(black)+color(black)51color(blue)-color(blue)51)`

`32-51=x`

`-19=x`

That's the number!