Answer:
Each roll of streamers is $2.50 and each package of balloons is $1.25.
Step-by-step explanation:
Let x represent the number of rolls of streamers and y represent the number of packages of balloons.
3 rolls of streamers, 3x, and 2 packages of balloons, 2y, cost 10.00; this gives us
3x + 2y = 10
2 rolls of streamers, 2x, and 1 package of balloons, 1y, cost 6.25; this gives us
2x + 1y = 6.25
This gives us the system of equations
[tex]\left \{ {{3x+2y=10} \atop {2x+1y=6.25}} \right.[/tex]
To solve this, we will use elimination. First we will make the coefficient of y the same. We will do this by multiplying the bottom equation by 2:
[tex]\left \{ {{3x+2y=10} \atop {2(2x+1y=6.25)}} \right. \\\\\left \{ {{3x+2y=10} \atop {4x+2y=12.50}} \right.[/tex]
We will eliminate y by subtracting the bottom equation from the top:
[tex]\left \{ {{3x+2y=10} \atop {-(4x+2y=12.5)}} \right. \\\\-1x=-2.5[/tex]
Divide both sides by -1:
-1x/-1 = -2.5/-1
x = 2.5
Each roll of streamers costs $2.50.
Substituting this back into the second equation, we have
2(2.5) + y = 6.25
5 + y = 6.25
Subtract 5 from each side:
5 + y - 5 = 6.25 - 5
y = 1.25
Each package of balloons costs $1.25.
