Alana is having a party. she bought 3 rolls of streamers and 2 packages of balloons for $10.00. she realized she needed more supplies and went back to the store and bought 2 more rolls of streamers and 1 more package of balloons for $6.25. how much did each roll of streamers and each package of balloons cost?

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

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:

We will eliminate y by subtracting the bottom equation from the top:

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.

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get