Question

The product of a number and 3 is 5 less than the quotient of a number and 3. What is the number?

Answer 1

The number `(n)` is `-15/8`

Explanation:

Let's break this down using mathematical symbols:

The product of a number and `3`:

We know that product means multiplication or times. A number is some unknown value which we can call a variable `n`. So this statement translates to `3timesn` or `3n`

is is an equilvent way to say equal to which can be represent using an `=` sign.

`5` less than the quotient of a number and `3`:

`5` less than means some quantity minus `5` which we can express as `"something"-5` for now. We also know that the quotient means division or divide`(divide)`. A number, as we said before is some unknown quantity (or number) that we can call a variable `n` that will be divided by `3`. Given this, the statement translates to

`n/3-5`

Putting the entire statement together we get an equation that we can solve for `n`

`3n=n/3-5`

So to solve for `n`, we can start by multiplying `3` to both sides

`3(3n)=3(n/3-5)`

`9n=(3n)/3-15`

`9n=n-15`

Subtract `n` from both sides

`9n-n=cancel(n-n)-15`

`8n=-15`

Divide `8` from both sides to solve for `n`

`cancel8/cancel8n=-15/8`

`n=-15/8`