SOLUTION: it takes a florist 3 h 15 min to make 3 small centerpieces and 3 large centerpieces. it takes 6 h 20 min to make 4 small centerpieces and 7 large centerpieces. how long does it tak

Question 1133486: it takes a florist 3 h 15 min to make 3 small centerpieces and 3 large centerpieces. it takes 6 h 20 min to make 4 small centerpieces and 7 large centerpieces. how long does it take to make each small centerpiece and each large centerpiece? write and solve a system of equations to find your answer.
Answer by ikleyn(52805) (Show Source): You can put this solution on YOUR website!
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Let x be the time for the florist to make 1 small centerpiece (in minutes), and
    
    y be the time for the florist to make 1 small centerpiece (in minutes).


Then from the condition you have this system of 2 equations in 2 unknowns.


    3x + 3y = 195   minutes   (1)    ( 105 minutes = 3 hours and 15 minutes )

    4x + 7y = 380   minutes   (2)    ( 380 minutes = 6 hours and 20 minutes )


Solve the system by the Elimination method in two steps.


STEP 1.   Divide the equation (1) (1) by 3 (both sides). Keep equation (2) as is. You will get the new system


     x +  y =  65             (3)   

    4x + 7y = 380             (4)      (eq4) is the same as eq(2) )  


STEP 2.  Multiply equation (1) by 4 (both sides). Then Subtract it from equation (4). You will get


     7y - 4y = 380 - 65*4

     3y      = 120           ==============>  y = 120/3 = 40 minutes.


Then from equation (1)  x = 65 - y = 65 - 40 = 25 minutes.


ANSWER.  25 minutes for small centerpiece  and  40 minutes for large centerpiece.

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