Question

How many ordered pairs of up(x,y) integers satisfy X/15=36/y

Answer 1

Answer:

Order pairs satisfying above equation are

(1,540), (540, 1) (2,270), (270, 2),(3,180), (180,3) (9,60), (60,9)

Step-by-step explanation:

Given that

$\frac{x}{15}=\frac{36}{y}$

cross multiplying both sides of above equation

$xy=36\times15$

xy = 540 .....(1

Now if we take (1,540) both sides of equation gets equal

(1)(540) = 540

540 = 540

Similarly if we take the order pairs (540, 1) (2,270),(3,180), (180,3) (270, 2), (9,60), (60,9) they also satisfy the above equation. So, these are all the order pairs that satisfy the above equation.

Answer 2

Answer:

48

Step-by-step explanation:

Given that  

\frac{x}{15}=\frac{36}{y}  

on cross multiplying both sides of above equation  

xy=36\times15  

xy = 540,

Now, that means xy are factors of 540=2²\times 3³\times 5

Total number of positive factors of 540 are (1+2)*(1+3)*(1+1)

=3*4*2 = 24.

Now if we chose x to be any of the factor then y should be 540/x.

Next, question is about integers since xy =540, either both x and y will be positive or both negative.

Hence total possible number of ordered pairs are 48.