# The sum of the quotient of a number and 3 and 8 is 16. What is the number?

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Nimo N. Share
Jan 30, 2018

See below.

#### Explanation:

The sum of the quotient of a number and 3 and 8 is 16."

One needs to translate from English to mathematics symbols. Sometimes, the words can be translated directly, piece by piece, from left-to-right, then the parts can be put together.

This one is one of those "left-to-right." translations:
$\left(\text{the first thing") + ("the second thing}\right)$

"is" translates to "=". So,
$\textcolor{b l u e}{\left(\text{the first thing") + ("the second thing}\right) = 16}$.

Using "x" for everything can make the eyes sore, so here we use "N" for the unknown Number.

the first thing:
"the quotient of a number and 3". Since "quotient of" means divide the first thing mentioned (an unknown number, N) by the second thing mentioned (3).
$N \div 3 = \frac{N}{3}$

We can fill-in part of the expression:
$\textcolor{b l u e}{\left(\frac{N}{3}\right) + \left(\text{the second thing}\right) = 16}$

the second thing:
The second thing being added is 8.

Now, finish the translation with a full equation:
$\textcolor{red}{\frac{N}{3} + \left(8\right) = 16}$

To solve the math problem, subtract 8 from both sides of the equation, then multiply both sides of the result by 3.

You should get:  color(red)( N = 24 .

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