A pencil costs $0.27 and a pen costs $0.32. You buy six pencils and the total cost is $4.18. How many pens did you buy?

1 Answer
Mar 19, 2018

No Sales Tax?? (Joke!) The answer is 8 pens

Explanation:

First, let's write the problem statement in an arithmetic form. If we're looking for a combination of pens and pencils, and know the cost of each:

#0.27c+0.32n=4.18#

#c# is the number of pencils purchased, and #n# is the number of pens. We know the number of pencils bought "You buy six pencils" and therefore know the value of #c#, #c=6#. Plugging that back into the equation:

#0.27xx6+0.32n=4.18 rArr 1.62+0.32n=4.18#

Now, we subtract 1.62 from both sides, effectively moving that number to the Right Hand Side (RHS):

#cancel(1.62-1.62)+0.32n=4.18-1.62#

#0.32n=2.56#

Finally, we divide the whole equation by #n#'s coefficient. In this case, that is 0.32:

#0.32/0.32n=2.56/0.32#

#color(red)(n=8#