If $3 a + 5 b = 132$ then the number of possible pairs of $a$ and $b,$ such that $a > b$ and $a$ and $b$ are positive integers is

Open in App

Solution

First find out the first pair which satisfy the given equation with minimum value of $b .$
It is $(39, 3)$

The other pairs can be calculated as for the equation, if we increase the value of $b$ by $1$ unit, then the value of $a$ must be decreased by $\frac{5}{3}$ unit.

We need values as positive integers only.
So if the value of $b$ is increased by 3 then the value of $a$ is decreased by $5$
Next pairs are $(34, 6), (29, 9), (24, 12), (19, 15)$
Next pair is $(14, 18)$ but $a > b$
So the last pair will be $(19, 15)$
So there are $5$ pairs which satisfy the given conditions.

Suggest Corrections

Similar questions

Q. If

3 a + 5 b = 132

then the number of possible pairs of

a

and

b,

such that

a > b

and

a

and

b

are positive integers is

Q. If a and b are positive real numbers such that 2 log (3a - 2b) = log a + log b, then the value of

\frac{a}{b}

Q. If a, b are positive integers such that a < b and

[a b] [\begin{matrix} a \\ b \end{matrix}] = 25,

then (a, b) = ____________.

Q. If a, b, c are positive integers such that

a + b + c \leq 8

then the number of possible values of the ordered triplet

(a, b, c)

for every pair of positive integers a and b there exist a unique pair of whole number q and r such that a=bq+r give examples of a and b whereever possible satisfying a) r=0 b) q=0 c) r>b d) if a< b what can be said about q and r

Join BYJU'S Learning Program

If 3a+5b=132 then the number of possible pairs of a and b, such that a>b and a and b are positive integers is

If $3 a + 5 b = 132$ then the number of possible pairs of $a$ and $b,$ such that $a > b$ and $a$ and $b$ are positive integers is