The number of solutions of the equation 3p + 4q = 70, where p and q are positive integers and p q, is

Question

The number of solutions of the equation 3p + 4q = 70, where p and q are positive integers and p > q, is

anonymous · Answer

$$3p = 70 - 4q$$

$$p = \frac{70 - 4q}{3}$$

As p and q are positive integers so,

Put q = 1, 2, 3  and so on so that the corresponding value of p is an positive integer..

Firstly put q = 1,

$$p = \frac{66}{3} = 22$$

Like wise you will get three values for p and q for which the equation holds true according to the condition, p>q.

These values are:
$$(p,q) = (22, 1), (4, 18), (7, 14)$$

So, number of solutions will be : 3..

ganeshie8 · Answer

correcting small typo ;)

These values are:
(p,q)=(22,1),(18, 4),(14, 7)

anonymous · Answer

Oh really thanks...@ganeshie8 ..