Question

amanda and james are selling flower bulbs for a school fundraiser. customers can buy packages of tulip bulbs and bags of daffodil bulbs. amanda sold 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. james sold 7 packages of tulip bulbs and 6 bags of daffodil bulbs for a total of $127. find the cost each of one package of tulips bulbs and one bag of daffodil

Explanation:

Step1: Define variables for costs

Let $x$ = cost of 1 tulip package, $y$ = cost of 1 daffodil bag.

Step2: Set up equations from sales

Amanda: $6x + 12y = 198$
James: $7x + 6y = 127$

Step3: Simplify Amanda's equation

Divide by 6: $x + 2y = 33$ → $x = 33 - 2y$

Step4: Substitute $x$ into James' equation

$7(33 - 2y) + 6y = 127$
Expand: $231 - 14y + 6y = 127$
Simplify: $231 - 8y = 127$

Step5: Solve for $y$

$-8y = 127 - 231$ → $-8y = -104$ → $y = \frac{-104}{-8} = 13$

Step6: Solve for $x$

$x = 33 - 2(13) = 33 - 26 = 7$

Answer:

One package of tulip bulbs costs $\$7$, and one bag of daffodil bulbs costs $\$13$.