Question

"Ava and Grace are selling flower bulbs for a fundraiser. Ava sold 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of 198. Grace sold 7 packages of tulip bulbs and 6 bags of daffodil bulbs for a total of 127. Use elimination to solve the system of linear equations and determine the cost of one package of tulips bulbs, x, and the cost of one bag of daffodil bulbs, y. Enter your answer as an ordered pair (x,y)."

Answer 1

To solve the system of linear equations representing the cost of flower bulbs, we can use the elimination method. The cost of one package of tulip bulbs is $3, and the cost of one bag of daffodil bulbs is $13.

Step-by-step explanation:

To solve this system of linear equations using elimination, we can multiply the equations by appropriate constants so that the coefficients of either x or y in both equations are opposite in sign. In this case, we can multiply the first equation by 7 and the second equation by 6 to eliminate the y terms.

Multiplying the first equation by 7 gives us 42x + 84y = 1386. Multiplying the second equation by 6 gives us 42x + 36y = 762.

Subtracting the second equation from the first equation, we get 48y = 624. Dividing both sides by 48, we find that y = 13.

Substituting this value of y back into either of the original equations, we can solve for x. Using the first equation, we have 7(6) + 12(13) = 198. Simplifying, we find that 42 + 156 = 198. Therefore, x = 3.

The cost of one package of tulip bulbs, x, is 3, and the cost of one bag of daffodil bulbs, y, is 13. Therefore, the ordered pair representing the cost of the bulbs is (3, 13).