Marcella and Rupert bought party stuff. Marcella bought 3 packs of ballooons and 4 packs of favors for a total of $14.63. Rupert bought 2 packs of balloons and 5 packs of favors for a total or $16.03. Find the price of each and write a system of equations to model this.
3B+4F=14.63
2B+5F=16.03
solve for B, and F with any number of methods.
To find the price of each pack of balloons and each pack of favors, we can set up a system of equations based on the given information.
Let's use the variable x to represent the price of each pack of balloons, and let y represent the price of each pack of favors.
Based on Marcella's purchase:
She bought 3 packs of balloons, so the cost for the balloons is 3x.
She also bought 4 packs of favors, so the cost for the favors is 4y.
The total cost for Marcella's purchase is $14.63, so we can write the first equation as:
3x + 4y = 14.63
Based on Rupert's purchase:
Rupert bought 2 packs of balloons, so the cost for the balloons is 2x.
He also bought 5 packs of favors, so the cost for the favors is 5y.
The total cost for Rupert's purchase is $16.03, so we can write the second equation as:
2x + 5y = 16.03
Now we have the system of equations:
3x + 4y = 14.63
2x + 5y = 16.03
To solve this system of equations, you can use substitution, elimination, or graphing methods.