If x/4+y/5=19/20 where x and y are positive integers then x+y is?

If you multiply through by 20 then you'll have 5x+4y=19 where x and y are positivie integers. Can you solve that? Hint: you only need to look at the integers less than 4.

Thanx a lot.

Modular arithmetic..

You're welcome! To solve the equation 5x+4y=19, we can start by considering the possible values for x and y that are less than 4, since x and y are positive integers.

Let's start by checking all possible values of x less than 4:

For x = 1, the equation becomes 5(1) + 4y = 19, which simplifies to 5 + 4y = 19.
Solving for y, we get y = (19 - 5) / 4 = 14 / 4 = 3.5, which is not a positive integer.

For x = 2, the equation becomes 5(2) + 4y = 19, which simplifies to 10 + 4y = 19.
Solving for y, we get y = (19 - 10) / 4 = 9 / 4 = 2.25, which is not a positive integer.

For x = 3, the equation becomes 5(3) + 4y = 19, which simplifies to 15 + 4y = 19.
Solving for y, we get y = (19 - 15) / 4 = 4 / 4 = 1, which is a positive integer.

Therefore, the only possible solution is x = 3 and y = 1.

To find x + y, we simply add the values of x and y together: 3 + 1 = 4. So, x + y = 4.

Therefore, if x/4 + y/5 = 19/20, where x and y are positive integers, then x + y = 4.