Question

Jacob and Caleb are selling flowers for a school fundraiser. Customers can buy packages of tulips and packages of roses. Jacob sold 3 packages of tulips and 5 packages of roses for a total of $152. Caleb sold 6 packages of tulips and 11 packages

of roses for a total of $323. Find the cost each of package of tulips and each package of roses.

Answer 1

To find the cost of tulip and rose packages, two linear equations were formulated from the sales of Jacob and Caleb. These equations were solved simultaneously, yielding that both tulip and rose packages cost $19 each.

Step-by-step explanation:

The question asks us to determine the cost of packages of tulips and roses based on the sales made by Jacob and Caleb for a school fundraiser. To find the cost of each package, we can set up a system of equations based on the information provided:

• Let T represent the cost of a package of tulips and R represent the cost of a package of roses.
• According to Jacob's sales, 3T + 5R = 152.
• According to Caleb's sales, 6T + 11R = 323.

We can solve these equations simultaneously to find the values of T and R. Multiplying the first equation by 2 gives us 6T + 10R = 304, which we can subtract from the second equation to eliminate T:

1. 6T + 11R - (6T + 10R) = 323 - 304
2. R = 19 - The cost for each package of roses.
3. Substitute the value of R into one of the original equations to find T:
4. 3T + 5(19) = 152
5. 3T + 95 = 152
6. 3T = 152 - 95
7. 3T = 57
8. T = 19 - The cost for each package of tulips.

Thus, each package of tulips and each package of roses costs $19.