Final answer:
The cost of one package of tulip bulbs is $5, and the cost of one bag of daffodil bulbs is $6. This was determined by setting up a system of equations based on the sales made by Brenda and Ryan and solving the system using the elimination method.
Step-by-step explanation:
To solve for the cost of one package of tulip bulbs and one bag of daffodil bulbs, we can set up a system of linear equations based on the information provided:
- Brenda sold 1 package of tulip bulbs (T) and 2 bags of daffodil bulbs (D) for a total of $17, which can be represented as T + 2D = 17.
- Ryan sold 8 packages of tulip bulbs (T) and 2 bags of daffodil bulbs (D) for a total of $52, which is represented as 8T + 2D = 52.
To find the values of T and D, we can use the method of substitution or elimination. Here, we will use the elimination method:
- Multiply the first equation by 4 to align the coefficients of D with the second equation: 4T + 8D = 68.
- Subtract the first equation from the second: (8T + 2D) - (4T + 8D) = 52 - 68, simplifying to 4T - 6D = -16.
- Now solve for T using the modified first equation: 4T = 68 - 8D.
- Substitute 4T from the modified first equation into the new equation obtained after subtraction, resulting in: (68 - 8D) - 6D = -16, which simplifies to 68 - 14D = -16.
- Solve for D: 14D = 84, thus D = 6. This means one bag of daffodil bulbs costs $6.
- Substitute the value of D back into one of the original equations to solve for T: T + 2(6) = 17, which simplifies to T + 12 = 17 and T = 5. This means one package of tulip bulbs costs $5.
Therefore, the cost of one package of tulip bulbs is $5, and the cost of one bag of daffodil bulbs is $6.