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By the help of algebra 1 we can find the ratio of two non- zero numbers. For example

**Example 1**: - If x : y = 2: 3, what is (4 x – y): (2 x + 3 y)?

**Solution**: - Given x : y = 2: 3, then x = 2 p, y = 3 p (p ≠ 0 is a common multiplier)

Therefore (4 x – y): (2 x + 3 y) = (4 x – y) / (2 x + 3 y)

= (4 * 2 p – 3 p) / (2 * 2p + 3 * 3p)

= (8 p – 3 p) / (4 p + 9 p)

= 5 p / 13 p

= 5 / 13

= 5 : 13

**Answer:** - Therefore **(4 x – y): (2 x + 3 y) = 5 : 13**

**Example 2**: If (3 x + 5 y ) : ( 7 x – 4 y) = 7 : 4, what is x : y?

**Solution**: -Given (3 x + 5 y): (7 x – 4 y) = 7: 4

Therefore (3 x + 5 y) / (7 x – 4 y) = 7 / 4

4 (3 x + 5 y) = 7 (7 x – 4 y)

12 x + 20 y = 49 x – 28 y

12 x – 49 x = -28 y – 20 y

- 37 x= - 48 y
Therefore (4 x – y): (2 x + 3 y) = (4 x – y) / (2 x + 3 y)

= (4 * 2 p – 3 p) / (2 * 2p + 3 * 3p)

= (8 p – 3 p) / (4 p + 9 p)

= 5 p / 13 p

= 5 / 13

= 5 : 13

Therefore (3 x + 5 y) / (7 x – 4 y) = 7 / 4

4 (3 x + 5 y) = 7 (7 x – 4 y)

12 x + 20 y = 49 x – 28 y

12 x – 49 x = -28 y – 20 y

x / y = 48 / 37

x : y = 48 : 37

Therefore x: y = 48: 37

x : y = 48 : 37

Therefore x: y = 48: 37