SOLUTION: Given that p is a whole number, and 1/4 < 2/p < 1/3, what is the value of p?

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Question 1179033: Given that p is a whole number, and 1/4 < 2/p < 1/3, what is the value of p?
Found 3 solutions by MathLover1, ikleyn, greenestamps:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

........divide by


............if so, then
and =>
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Your starting inequality is

     <  < 


It is so called "compound inequality", and it is equivalent to two separate inequalities


     <     (1)

and

     < ,   (2)


connected by the service word "and".


From inequality (1), multiplying both sides by positive number 4p, you get an EQUIVALENT inequality

    p < 4*2 = 8.    (3)



From inequality (2), multiplying both sides by positive number 3p, you get an EQUIVALENT inequality

    p > 3*2 = 6.    (4)



So, from (3) and (4) you have

    6 < p < 8.


There is only one integer number, satisfying this compound inequality :  p = 7.    ANSWER

Solved.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The algebraic solutions from the other tutors are fine.

But this problem is easily solved using a technique that is occasionally useful in comparing fractions.

In most problems where fractions are being compared, it is easiest to get a common denominator. But in a few kinds of problems, like this one, a solution is obtained more easily by making the numerators the same.

So in this problem convert the 1/4 and 1/3 into equivalent fractions with numerator 2, as in the fraction 2/p. Then you have



From there the solution is trivial....

ANSWER: p=7
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