14 shrubs + 9 roses = $190 and 9 shrubs + 12 roses = $210

Question

14 shrubs + 9 roses = $190 and 9 shrubs + 12 roses = $210

 

Answer 1

14 shrubs + 9 roses = $190      (eqn 1.)

9 shrubs + 12 roses = $210      (eqn 2.)

 

we can make coefficient of shrubs /roses(do it for only one of them) equal by multiplying both equations with an appropriate number.I am going to make the coefficient of roses equal in both the eqations 

 

LCM of 9 and 12 = 36

eqn 1. multiplied by 4   :  56 shrubs + 36 roses = 760

eqn 2. multiplied by 3   :  27 shrubs + 36 roses = 630      , substitute this equation from above we get

 

                                   56 shrubs - 27 shrubs = 760-630   (as roses term will be cancelled out as they have equal numbers)

                                    29 shrubs = 130

                                        shrubs = 130/29 = $4.48

 

 9 shrubs + 12 roses = $210  

9*4.48  + 12 roses = 210

 40.32 + 12 roses = 210 

              12 roses = 210 - 40.32 =169.68

                   roses =169.68/12 = $14.14  

 

Cost of shrubs = $4.48

 cost of roses   = $14.14