SOLUTION: Write the following phrase using symbols. Use the variable p to represent the number in each case. 2 more than 6 times a number divided 3

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Question 75763: Write the following phrase using symbols. Use the variable p to represent the number in each case.
2 more than 6 times a number divided 3
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
2 more than 6 times a number divided 3
.
This is a good example of why must be careful in what you say in mathematics. This problem
can be interpreted in several ways because the person who wrote it thought they were being
clear when they really were not.
.
For example. I could write that 2 more than 6 is 8 and then you are to multiply that by a
number (p) divided by 3. The result would be:
.
%282%2B6%29%2A%28p%2F3%29
.
and this would simplify to
.
8p%2F3
.
Or I could also interpret the problem as being the quantity (2 more than 6p) divided by 3 which would be
written as
.
%282+%2B+6p%29%2F3 which simplifies to %282%2F3%29+%2B+2p
.
Or I could also interpret the problem as 2 being added to the quantity 6p divided by 3
which is written:
.
2+%2B+%286p%2F3%29 which simplifies to 2+%2B+2p
.
and there is no way to tell which one of these is correct because the writing can have
at least these three interpretations. It always to say things such as "the quantity ..."
which helps the reader to group things appropriately.
.
For example if you said 2 is added to the quantity 6 times a number and the resulting
quantity is divided by 3, it would be hard to interpret the problem as anything other than
.
%282+%2B+6p%29%2F3
.
Hope this helps you to understand why the tutors on this site sometimes have difficulty
understanding what the problem means. Ask your teacher what the answer is supposed to
be and see what the original writer of the problem intended. Also ask your teacher if
the writing can be interpreted in the above several ways.
.
By the rules of operations, if the problem were written as:
.
2 + 6 * p / 3
.
you would first do the multiplications and divisions in order from left to right so the
problem would be:
.
2+%2B+%286p%29%2F3 which, as shown above, simplifies to 2 + 2p.