Algebra 1 Answers

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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
           x / y = 48 / 37
           x : y = 48 : 37
Therefore x: y = 48: 37
 




 

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