How many pairs of positive integers (x,y) have the property that the ratio x : 4 equals the ratio 9 : y ?

piger Aug 9, 2023

#1**0 **

Read the pairs of positive integers (x, y) from left to right:

x : 4 = 9 : y

(36, 1) , (18, 2) , (12, 3) , (9, 4) , (6, 6) , (4, 9) , (3, 12) , (2, 18) , (1, 36)> = 9 such pairs

The pairs mean: [x : 4] = [9 : y] = [36 : 4] =[9 : 1]

Guest Aug 9, 2023

#2**0 **

To solve this, we can set up a proportion equation:

x / 4 = 9 / y

Cross-multiplying gives:

xy = 36

Now, we need to find the pairs of positive integers (x, y) that satisfy this equation. The pairs that work are:

(1, 36), (2, 18), (3, 12), (4, 9), (6, 6), (9, 4), (12, 3), (18, 2), (36, 1)

So, there are 9 pairs of positive integers (x, y) that satisfy the given property.

Therefore, the required pair of positive integers (x,y) satisfied the given property is 9.

tastyabananas2ndDad Aug 10, 2023