SOLUTION: Kaiden has sold 10 bunches of roses and 12 violets for a total of $380. Grayson has sold 6 bunches of roses and 8 violets for $244. What is the cost of a bunch of roses? What is th

Algebra ->  Equations -> SOLUTION: Kaiden has sold 10 bunches of roses and 12 violets for a total of $380. Grayson has sold 6 bunches of roses and 8 violets for $244. What is the cost of a bunch of roses? What is th      Log On


   

Question 1102672: Kaiden has sold 10 bunches of roses and 12 violets for a total of $380. Grayson has sold 6 bunches of roses and 8 violets for $244. What is the cost of a bunch of roses? What is the cost of a bunch of violets? How much would it cost Mac to purchase 2 bunches of roses and 3 violets?
Answer by ikleyn(52777) About Me  (Show Source):
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Kaiden has sold 10 bunches of roses and 12 violets for a total of $380. Grayson has sold 6 bunches of roses and 8 violets for $244.
What is the cost of a bunch of roses? What is the cost of a bunch of violets? How much would it cost Mac to purchase
2 bunches of roses and 3 violets?
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The condition gives you this system of 2 equations in 2 unknowns 

10x + 12y = 380     (1)
 6x +  8y = 244     (2)


I will solve it by the Elimination method. For it, multiply eq(1) by 3 (both sides). Multiply eq(2) by 5. You will get

30x + 36y = 1140    (3)
30x + 40y = 1220    (4)


Next subtract eq(3) from eq(4).  The terms "30x" will cancel each other, and you will get a single equation for "y":

4y = 1220 - 1140 = 80  ====>  y = 80%2F4 = 20.


Then from eq(1)  10x = 380 - 12*20 = 140  ====>  x = 140%2F10 = 14.


Answer.  Bunch of roses costs $14.  Each violet costs $20.

         2 bunches of roses and 3 violets cost 2*$14 + 3*$20 = $88.