Marcella and Ruben bought some party supplies. Marcella bought 3 packages of
balloons and 4 packages of favors for $14.63. Ruben bought 2 packages of balloons and
5 packages of favors for $16.03. Find the price of a package of balloons.
3 b + 4 f = 14.63
2 b + 5 f = 16.03
solve the system for b
15 b + 20 f = 73.15
8 b + 20 f = 64.12
subtracting equations (to eliminate f) ... 7 b = 9.03
To find the price of a package of balloons, we can set up a system of equations based on the given information.
Let's assume the price of a package of balloons is x dollars.
According to the information given, Marcella bought 3 packages of balloons and 4 packages of favors for a total of $14.63. Therefore, we can set up the equation:
3x + 4y = 14.63, where y represents the price of a package of favors.
Similarly, Ruben bought 2 packages of balloons and 5 packages of favors for a total of $16.03. Therefore, we can set up the equation:
2x + 5y = 16.03.
Now we have a system of equations:
3x + 4y = 14.63
2x + 5y = 16.03
To solve this system, we can use either substitution or elimination.
Let's use the elimination method to solve the system:
Multiply the first equation by 2 and the second equation by 3 to eliminate the x variable:
6x + 8y = 29.26
6x + 15y = 48.09
Subtract the first equation from the second equation:
6x + 15y - (6x + 8y) = 48.09 - 29.26
7y = 18.83
y = 18.83 / 7
y ≈ 2.69
Now that we have the value of y, we can substitute it back into one of the original equations to find x:
2x + 5y = 16.03
2x + 5(2.69) = 16.03
2x + 13.45 = 16.03
2x = 16.03 - 13.45
2x ≈ 2.58
x = 2.58 / 2
x ≈ 1.29
Therefore, the price of a package of balloons is approximately $1.29.