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

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#