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):
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
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
